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Physics Questions and Answers October 31, 2022

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For an ideal gas consisting of N distinguishable particles in a volume V, the probability of finding exactly 2 particles in a volume partialV

The Hamiltonian of a system of 3 spins is HJ (S1S2 S2S3), where St 1 for i1,2,3. Its canonical partition function, at temperature T, is

A certain twodimensional solid crystallizes to a square monoatomic lattice with lattice constant a. Each atom can contribute an integer number of free conduction electrons. The minimum number of electrons each atom must contribute such that the free electron Fermi circle at zero temperature encloses the first Brillouin zone completely, is

A tight binding model of electrons in one dimension has the dispersion relation epsilon(k) 2t(1cos ka), where t0, a is the lattice constant and pia

A lattice is defined by the unit vectors , a1 ai,a2a2ia32 j and a3ak, where a0 is a constant. The spacing between the (100) planes of the lattice is

A spacecraft of mass m 1000 kg has a fully reflecting sail that is oriented perpendicular to the direction of the sun. The sun radiates 1026 W and has a mass M 1030 kg. Ignoring the effect of the planets, for the gravitational pull of the sun to balance the radiation pressure on the sail, the area of the sail will be.

The Greens function for the differential equation d2xdt2xf(t), satisfying the initial conditions x(0)dxdt(0)0 is The solution of the differential equation when the source f(t)0(t) (the Heaviside step function) is

The solution of the differential equation (dydx)2 d2ydx2 ey, with the boundary conditions y(0)0 and y(0)1 is.

If we take the nuclear spin into account, the total angular momentum is F LSI, where I and S are the orbital and spin angular momenta of the electron. The Hamiltonian of the hydrogen atom is corrected by the additional interaction (L5), where 0 is a constant. The total angular momentum quantum number F of the p orbital state with the lowest

The absorption lines arising from pure rotational effects of HCI are observed at 83.03 cm, 103.73 cm, 124.30 cm, 145.03 cm and 165.51 cm. The moment of inertia of the HCI molecule is (take 5.6x10 kgm).

The energies of the 3 lowest states of an atom are E 14 eV, E, 9 eV and E 7 eV. The Einstein coefficients are A10 3x108 , A201.2x108 s and A21 8x107 s. If a large number of atoms are in the energy level E2, the mean radiative lifetime of this excited state is

Two voltmeters A and B with internal resistances 2Mohm and 0.1kohm are used to measure the voltage drops VA and VB, respectively, across the resistor R in the circuit shown below. The ratio VAVB is

The IV characteristics of the diode D in the circuit below is given by II(eqVekT 1) where I, is the reverse saturation current, V is the voltage across the diode and T is the absolute temperature. if the input voltage is Vin, then the output voltage Vout is.

Consider a concave mirror and a convex lens (refractive index 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification M. When the setup is kept in a medium of

An infinitely long uniform line charge distribution of charge per unit length lies parallel to the yaxis in the 3 yz plane at z a (see figure). If the magnitude of 2 the flux of the electric field through the rectangular surface ABCD lying in the xy plane with its center at AL the origin is (o permittivity of free space), then no the value of n

A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it reaches its maximum height, its acceleration due to the planets gravity is 14th of its value at the surface of the planet. If the escape velocity from the planet is Vesc V N, then the value of N is (ignore energy loss due to atmosphere)

Two identical uniform discs roll without slipping on two different surfaces AB and CD (see figure) starting at A and C with linear speeds v and v2, respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and v 3 ms, then v in ms is (g 10 ms) V 3ms 30 m B Ci V 27 m

Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10 times the power emitted from B. The ratio (AB) of their wavelengths A and B at which the peaks occur in their respective radiation curves is

A nuclear power plant supplying electrical power to a village uses a radioactive material of half life T years as the fuel. The amount of fuel at the beginning is such that the total power requirement of the village is 12.5 of the electrical power available form the plant at that time. If the plant is able to meet the total power needs of the

A Youngs double slit interference arrangement with slits S and S is immersed in water (refractive index 43) as shown in the figure. The positions of maxima on the surface of water are given by x pm2 d, where is the wavelength of light in air (refractive index 1), 2d is the separation between the slits and m is an integer. The value of p is S S

For photoelectric effect with incident photon wavelength 2, the stopping potential is Vo. Identify the correct variation(s) of Vo with 2 and 12. (A) (B) (C) Z 12 (D) 2 12

Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two

Plancks constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are) (A) M c (C) L h (B) Mo G (D) Lx G

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies and 2 and have total energies E, and E2, respectively. The variations of their momenta p with positions x are shown in the figures. If n and n, then the correct equation(s) is(are) a a b R (A) E00, E00 (C) 0,0 n b P Energy E (B) (D) 00

A ring of mass M and radius R is rotating with angular speed o about a fixed vertical axis passing through its centre O with two point masses each of mass M at rest at O. These masses can move radially outwards along two massless 8 rods fixed on the ring as shown in the figure. At some instant the angular speed 8 of the system is and one of the

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density are kept parallel to each other. In their resulting electric field, point charges q and q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small

Two identical glass rods S and S (refractive index 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S on its axis at a distance of 50 cm from the curved face,

A conductor (shown in the figure) carrying constant current I is kept in the xy plane in a uniform magnetic field B. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are) I RR TU6 TU4 LRR (A) If B is along 2, Fx (LR) (C) If B is along y, Fx (LR) y X L (B) If B is along x, F 0 (D) If B is

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is(are) (A) The average energy per mole of the gas mixture is 2RT. (B) The ratio of speed of sound in the gas mixture to that in helium gas is 65. (C) The ratio of the rms

In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are 2.7 108 2 m and 1.0 107 m, respectively. The electrical resistance between the two faces P and Q of the composite bar is (A) (C) 2475 64 1875 49 452 Al Fe 2mm P 7 mm (B) (D)

Match the nuclear processes given in column I with the appropriate option(s) in column II Column I Column II 235 Absorption of thermal neutrons by 92 (A) Nuclear fusion (B) (C) Fission in a nuclear reactor Bdecay (D) yray emission (P) (Q) (R) (S) (T) 60Co nucleus 27 U Energy production in stars via hydrogen conversion to helium Heavy water

A particle of unit mass is moving along the xaxis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and U are constants). Match the potential energies in column I to the corresponding statement(s) in column II. Column I Column II (A) (B) U(x) 1 U 2

if a stone of mass 0.25kg tied to a string executes uniform circular motion with a speed of 2 ms of radius 3m, what is the magnitude of tensional force acting on the stone

What is the acceleration of system shown in the figure below if the coefficient of kinetic friction is 0.10 Assume that the blocks start from rest, 30 degrees, and that m12.0 kg, m25.0 kg.

A concave mirror produces three times. magnified (enlarged) (enlarged) real image object, placed at an of front of it. 10cm L is the image located se

Consider the transfer function of a CT system given by 1.403 s(s12) G(s) Using a zeroorder hold with T 0.01, the transfer function G(z) of the correspond ing sampleddata system is given by G(z) 6.7426 x 105. Yk z 0.9608 (z1)(z 0.8869) Show that a controllable and observable statespace realization of the system is given by Ik1 i Ik 0 1

A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 0.005)m, the gas in the tube is (Useful information 167RT 640 J2

At time t 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) Io cos (ot), with Io 1A and co 500 rads starts flowing in it with the initial direction shown 7 in the figure. At t , the key is switched from B to D. Now onwards only A and D are connected. A 600 total charge Q flows from the

E A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 13 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C. When the capacitor is charged, the plate area covered by the dielectric gets charge Q

One end of a taut string of length 3m along the x axis is fixed at x 0. The speed of the waves in the string is 100 ms. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are) TTX 50nt (A) y(t) A sin (B) y(t) A sin 6 3 250nt 3 (C)

A transparent thin film of uniform thickness and refractive index n 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f from

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the sam material, each of length L and diameter 2d. The way these wires are connected is given in the options How much time in minutes will it

Two ideal batteries of emf V and V and three resistances R, R and R3 are connected as shown in the figure. The current in resistance R would be zero if (A) V V and R R R3 (B) V V and R 2R R (C) V 2V and 2R 2R R3 (D) 2V V and 2R R R V R R3 www www V J

Let E (r), E (r) and E3(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density 2, and an infinite plane with uniform surface charge density o. If E (r) E (r) E (r) at a given distance ro, then (A) Q 4onr (C) E, (r2) 2E (12) 2 2 (D) E (r2) 4E3 (12) (B)

A light source, which emits two wavelengths 2 400 nm and 22 600 nm, is used in a Youngs double slit experiment. If recorded fringe widths for 2 and 22 are and B and the number of fringes for them within a distance y on one side of the central maximum are m and m2, respectively, then (A) B B (B) m m (C) From the central maximum, 3rd maximum of

In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle 0 with the horizontal floor. The coefficient of friction between the wall and the ladder is and that between the floor and the ladder is u. The normal reaction of the wall on the ladder is N and that of the floor is N. If the ladder is

During Searles experiment, zero of the Vernier scale lies between 3.20 x 102 m and 3.25 x 10 m of the main scale. The 20th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 x 102 m and 3.25 x102 m of the

Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively as shown in the figure. The speed of A is 1003 ms . At time t 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion

A thermodynamic system is taken from an initial state i with internal energy U 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are Waf 200 J, Wib 50 J and Wbf 100 J respectively. The heat supplied to the system along the path iaf,

Two parallel wires in the plane of the paper are distance Xo apart. A point charge is moving with speed u between the wires in the same plane at a distance X from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R. In contrast, if the currents I in the

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density p of the fog, intensity (powerarea) S of the light from the signal and its frequency f. The engineer finds that d is proportional to Sn. The value of n is

A rocket is moving in a gravity free space with a constant acceleration of 2 ms2 along x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in x direction with a speed of 0.3 ms relative to the rocket. At the same time, another ball is thrown in x direction with a speed of

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 2 resistance, it 2n can be converted into a voltmeter of range 030 V. If connected to a resistance, it becomes an 249 ammeter of range 01.5 A. The value of n is

A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular

Consider an elliptically shaped rail PQ in the vertical plane with OP 3 m and OQ 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the 4m kinetic energy of the block when it reaches Q is (n10) Joules. The value of n is

A particle of mass 3.5kg is released from rest and slides down a smooth inclined plane at arcsin to the horizontal. Find the distance travelled when the particle increases velocity to 5ms.

A ball of mass 1.5kg is projected up a rough plane inclined at 30 0 to the horizontal with a velocity of 4m/s. Given that =0.2. Find the distance the particle moves before coming to rest.

A car of mass 1400kg moving up a hill of slope arc sin(1/12) at a constant speed of 25m/s . If the power dissipated by the engine is 32kW. Find the resistance to the motion. At the top of the hill , the slope becomes horizontal. Find the initial acceleration given that the opposing resistance remains unchanged.

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R2, R and 2R respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are E, E and E3 respectively, then P Sphere 1 (A) E E E3 R2 2Q R Sphere 2 (A) E3 E E 4Q (C) E E

A glass capillary tube is of the shape of truncated cone with an apex angle a so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is p, and its contact angle with glass is 0, the

If Acu is the wavelength of K, Xray line of copper (atomic number 29) and 2Mo is the wavelength of the Ka Xray line of molybdenum (atomic number 42), then the ratio cuMo is close to (B) 2.14 (A) 1.99 (C) 0.50 (D) 0.48

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately The

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u and u, respectively. If the ratio u u 21 and hc 1240 eV nm, the work function of the metal is nearly (B) 3.2 eV (A) 3.7 eV (C) 2.8 eV (D) 2.5 eV

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90 2, as shown in the figure. The least count of the scale used in the metre bridge is 1 mm. The unknown resistance is (A) 60 0.1552 R www. 40.0cm (B) 135 0.560 9092 www. (C) 600.2552 (D) 135 0.2302

Parallel rays of light of intensity I 912 Wm2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take StefanBoltzmann constant o 5.710 Wm K and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to (A) 330 K (B) 660 K (C)

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counterclockwise direction if seen from above. Wire I P d S Wire 2 R,When d

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counterclockwise direction if seen from above. Wire I P d S Wire 2

In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows

If the piston is pushed at a speed of 5 mms, the air comes out of the nozzle with a speed of (A) 0.1 ms (B) 1 ms (C) 2 ms (D) 8 ms ,A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lifts motion is given in List I and the distance where the water jet hits the floor of the

Four charges Q, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x 2a, a, a and 2a, respectively. A positive charge q is placed on the positive y axis at a distance b0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select

Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists. List I List II P. Q. R. S. Code (A) P1, Q2, R3, S4

A block of mass m 1 kg another mass m 2kg, are placed together (see figure) on an inclined plane with angle of inclination 0. Various values of 0 are given in List I. The coefficient of friction between the block m, and the plane is always zero. The coefficient of static and dynamic friction between the block m and the plane are equal to 0.3.

A particle of mass m, which moves freely inside an infinite potential well of length a is initially in the state psi(mu.0)35a sin(3pi mua) 15a sin (5 pi xa) (a) Find psi (mu,t) at any later time t. (b) calculate the probability density p(x,t) and the current density J(x,t).

A 200 kg batch of granular solids containing 30 per cent of moisture is to be dried in a tray dryer to 15.5 moisture by passing a current of air at 350 K tangentially across its surface at the velocity of 1.8 ms. If the constant rate of drying under these conditions is 0.7 gsm2 and the critical moisture content is 15, calculate the approximate

A large cylindrical water tank 11.5 m in diameter and 13.5 m tall is supported with its base 8.75 m above the ground by a stand as shown in the figure. The water level in the tank is 10.6 m deep, and the density of the water in the tank is 1.00 gcm. A very small hole is formed at the base of the vertical wall of the tank, and water is squirting

An open circular tank 5 m diameter contains benzene at 22 deg Celsius exposed to atmosphere in such a manner that the liquid is covered with air film of 0.9102 m thickness. The concentration of benzene beyond the air film is negligible. If benzene costs Rs. 80 per litre, calculate amount lost per day. Data Vapor pressure of benzene at 22 deg

Find the speed of an electron a kinetic energy of 2.07 eV. 1.602 x 1019 J. Answer in units of ms. that has 1 eV

Calculate the speed of a proton with a kinetic energy of 2.07 eV. Answer in units of ms.

A parallelplate capacitor has a capacitance Co. A second parallelplate capacitor has plates with twice the area and twice the sepa ration. What is the capacitance of the second ca pacitor

Calculate the energy stored in a 27.3 F capacitor when it is charged to a potential of 82 V. Answer in units of m.J.

The longest distance recorded in the sport of bale throwing is 81.1 m. It was achieved by Steve Turner of the United States in 1981. Assuming the initial launch angle was 45, omitting air resistance, establish a) the initial speed of the projectile and b) the total time of flight of the projectile c) qualitatively how would the answers if the

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is (B) 0.50 (D) 4.00 (A) 0.25 (C) 2.00

X y (K being a constant of 1 appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the xy plane is (x y 3 (x y 50 (K i 2K (A) The work done on a particle of mass m by a force K (C) a 2a (B) a (D) 0

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity and the other 2k. The temperature difference between the ends along the xaxis is the same in both the configurations. It takes 9 s to transport a certain amount of

A ray of light travelling in the direction (133) is incident on a plane mirror. After reflection, it travels along the direction (i3). The angle of incidence is (A) 30 (C) 60 (B) 45 (D) 75

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter

Two nonreactive monoatomic ideal gases have their atomic masses in the ratio 2 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 3. The ratio of their densities is (A) 14 (B) 12 (C) 69 (D) 89

In the Youngs double slit experiment using a monochromatic light of wavelength 2, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is (A) (2n1) (B) (2n1) (C) (2n1) (D) (2n1) 8 4 2 16

The image of an object, formed by a planoconvex lens at a distance of 8 m behind the lens, is real and is 2 onethird the size of the object. The wavelength of light inside the lens is times the wavelength in free 3 space. The radius of the curved surface of the lens is (A) 1 m (B) 2 m (C) 3 m (D) 4 m

A particle of mass m is projected from the ground with an initial speed up at an angle a with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed uo. The angle that the composite system makes

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 x 108 ms. The final momentum of the object is 1 (B) 1.0 107 kg ms (A) 0.3 x 107 kg ms (C) 3.0 x 107 kg ms (B) 9.0 107 kg ms

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S is pressed first to fully charge the capacitor C and then released. The switch S is then pressed to charge the capacitor C. After some time, S is released and then S3 is pressed. After some time, (A) the charge on the upper plate of C is

A particle of mass M and positive charge Q, moving with a constant velocity u, 4ms, enters a region of uniform static magnetic field normal to the xy plane. The region of the magnetic field extends from x 0 to x L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity

A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation y(x, t) 0.01m sin (62.8m )x cos(628s )t. Assuming 3.14, the correct statement(s) is (are) (A) The number of nodes is 5. (B) the length of the string is 0.25 m. (C) The maximum displacement of the midpoint of the string, from its

A solid sphere of radius R and density p is attached to one end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3p. The complete arrangement is placed in a liquid of density 2p and is allowed to reach equilibrium. The correct statement(s) is (are) (A) the net

Two nonconducting solid spheres of radii R and 2R, having uniform volume charge densities p and p2 respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centre of the spheres is zero. The ratio pp2 can be 32 (A)4 (B) 25 (C) 32 25 (D) 4

A bob of mass m, suspended by a string of length 1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length 12, which is initially at rest. Both the strings are massless and inextensible. If the second bob, after

A freshly prepared sample of a radioisotope of halflife 1386 s has activity 10 disintegrations per second. Given that In 2 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is