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Physics Questions and Answers September 16, 2022

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A onedimensional infinite region

The setting of this question is an ndimensional manifold M equipped with metric tensor gj and covariant derivative Va. We work in a local coordinate system X. Let C be a curve written as X (A) and let its tangent vector be Ti (a) Consider a vector V evaluated along the curve C and define AV V (X (XSX)) V (X(A)) where SX 1. Write AV in terms of

The RobertsonWalker geometry (to be discussed in Chapter 9) has a spacetime interval ds dta(t) dx sin x (do sin0do) where the coordinates are x t, x x, x 0, x 0, and a(t) is a function of time. (a) Calculate all the Christoffel symbols Im with purely spatial indices that is, with indices from 1 to 3. (b) A covariant vector with components b

You paralleltransport a contravariant vector A around the circle r 6GM, 0 2 in the Schwarzschild geometry (see the preceding problem). If the vector initially has components A (0, 1, 0, 0), what will be its components after it has been transported around the circle Assume that the transport is instantaneous (dt 0).

The spacetime interval in the interior of a uniform spherical mass distribution of mass M and radius R is, in the linear approximation, ds (1 20)dt (1 20)dr rd0 r sin 0do where GMr2R 3GM2R is the Newtonian potential. Find a formula for the volume of a concentric sphere of radius r R. Assume that 1, so 1 20 1 .

A curved spacetime has a spacetime interval ds A(r)dt B(r)dr C(r)(rd0 r sin 0dp) where r, 0, and are spherical coordinates, and where A(r), B(r), and C(r) are given functions of r. Show that (a) The circumference of the circle r r is 2C(ri)r. (b) The area of the sphere r r is 4trC(ri).

The equation z (x) (y) defines a paraboloid of revolution. The surface of this paraboloid is a 2D curved space, whose points can be described by the coordinates x (x) (y)2 and x 0, where is the usual azimuthal angle measured around the zaxis. In terms of these coordinates, the space interval has the form dl guvdxdx, with , v 1, 2. (a) What

The Lie derivative of a contravariant vector x is (a) Show that LEX lim 80 (a) Show that xa and verify that this has the alternative form xa x(x) X (x) E LEX(x) a (b) Show that L Xx. The Lie derivative of a contravariant tensor Avis LAV lim 80 LEX(x) X aX Av LAVa xa xa and verify that this has the alternative form Av (x) A(x) E LAVA

Show that for a vector Au Av Aviu Show that for a tensor Au, Aviu Au.v Av.l Aav Aav R BuvAao Rav Ao

If the momentum of a body increases by 0.01, its kinetic energy will increase by (a) 0.01 (b) 0.02 (c) 0.04 (d) 0.08

If the momentum of a body is increased by 100, then the percentage increase in the kinetic energy is (c) 225 (a) 150 (b) 200 (d) 300

A particle of mass m is moving in a horizontal circle of k radius r, under a centripetal force equal to k is constant. The total energy of the particle is k k k 2k 2r (a) r (b) (c) 2r (d) where r

A body of mass 5 kg is moving with a momentum of 10 kg ms. A force of 0.2 N acts on it in the direction of motion of the body for 10 seconds. The increase in its kinetic energy is (a) 2.8 J (b) 3.2 J (c) 3.8 J (d) 4.4 J

Two masses of 1g and 9g are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is (a) 19 (b) 91 (c) 13 (d) 31

A body of mass 2kg is thrown upward with an energy 490 J. The height at which its kinetic energy would become half of its initial kinetic energy will be g9.8 ms (a) 35m (b) 25 m (c) 12.5 m (d) 10m

Two carts on horizontal straight rails are pushed apart by an explosion of a powder charge Q placed between the carts. Suppose the coefficients of friction between the carts and rails are identical. If the 200 kg cart travels a distance of 36 metres and stops, the distance covered by the cart weighing 300 kg is 200kg 300 kg O (a) 32 metres (b) 24

A ball bounces to 80 of its original height. What fraction of its potential energy is lost in each bounce (a) 0.20 (b) 0.60 (c) 0.40 (d) 1

An unloaded bus and a loaded bus are both moving with the same kinetic energy. The mass of the latter is twice that of the former. Brakes are applied to both, so as to exert equal retarding force. Ifx, x, be the distance covered by the two buses respectively before coming to a stop, then (a) x x (b) 2xx (c) 4xx (d) 8x x 2

A bus can be stopped by applying a retarding force F when it is moving with a speed v on a level road. The distance covered by it before coming to rest is s. If the load of the bus increases by 50 because of passengers, for the same speed and same retarding force, the distance covered by the bus to come to rest shall be (a) 1.5 s (b) 2 s (c) 1

(a) 10V (b) 25 V (c) V 5 (d) 5 V,When a long spring is stretched by 2cm, its potential energy is V. If the spring is stretched by 10 cm, the potential energy in it will be

A particle which is constrained to move along the x axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F (x) kx ax. Here k a are positive constants. For x0, the functional from the potential energy Ux) of the particle is U (a) (c) Up X X U (b) mes h U (d) X

One ma takes 1 minute to raise a box to a height of 1 1 meter and another man takes minute to do so. The energy of the two is (a) different (c) energy of the first is more (d) energy of the second is more (b) same

The potential energy of a system is represented in the first figure. The force acting on the system will be represented by UMA (a) (c) Fox) H FA U a x X (b) (d) Foo Foo X a D X X

A particle moves in a potential region given by U 8x 4x 400 J. Its state of equilibrium will be (a) x25m (b)x0.25 m (c)x0.025 m (d)x2.5m

A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time t is proportional to (a) 2 (b) t (c) 2 (d)

Two men with weights in the ratio 43 run up a staircase in time in the ratio 1211. The ratio of power of the first to that of second is 4 (a) 3 Im (b) 12 11 (c) 48 33 9

A spring of spring constant 5 x 10 Nm is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is (a) 6.25 Nm (c) 18.75 Nm (b) 12.50 Nm (d) 25.00 Nm

Two springs of spring constants 1500 Nm and 3000 N m respectively are stretched with the same force. They will have potential energy in the ratio (a) 41 (b) 14 (c) 21 (d) 12

A ball of mass M falls from a height h on a floor which the coefficient of restitution is e. The height attained by the ball after two rebounds is (a) eh (b) eh (c) eh h

A body is attached to the lower end of a vertical spiral spring it is gradually lowered to its equilibrium position. This stretches the spring by a length x. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case. (a) x (b) 2x (c) 3x (d) X

The face of a dam is a vertical rectangle of height 100 ft. and width 200 ft. Find the total fluid force exerted on the face when the water surface is level with the top of the dam.

Two equal masses are attached to the two ends of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over its natural length. The work done by the spring on each mass is 1 (a) kx (b) kx (c) kx 77 1 1 (d) 4kx

Two protons are situated at a distance of 100 fermi from each other. The potential energy of this system will be in eV. (a) 1.44 (b) 1.44 10 (c) 1.4410 (d) 1.44 104

80Hg208 nucleus is bombarded by aparticles with velocity 107 ms. If the aparticle is approaching the Hg nucleus headon then the distance of closest approach will be (a) 1.115 103 m (c) 111.5x 1013 m (b) 11.15 x 1013 m (d) zero

A force (412) N acting on a body maintains its velocity at (223) ms. The power exerted is (a) 4 W (b) 5 W (c) 2 W (d) 8 W

An adult weighing 600 N raises the centre of gravity of his body by 0.25 m while taking each step of Im length in jogging. If he jogs for 6 km, the energy utilised by him in jogging is (a) 9106J (b) 9105J (c) 6106J (d) 6 10J

Water is flowing in a river at 2 ms. The river is 50m wide and has an average depth of 5 m. The power available from the current in the river is (Density of water 1000 kg m) (a) 0.5 MW (b) 1 MW (c) 1.5 MW (d) 2 MW

A body is falling under gravity. When it loses a gravita tional potential energy by U, its speed is v. The mass of the body shall be (a) 2U V (b) U 2v 2U (c) U (d) 21

The power of a water pump is 2 kW. If g 10 ms , the amount of water it can raise in one minute to a height of 10 mis (a) 2000 litre (b) 1000 litre (c) 100 litre (d) 1200 litre

A liquid of density d is pumped by a pump P from situation (i) to situation (ii) as shown in the diagram. If the cross section of each of the vessels is a, then the work done in pumping (neglecting friction effects) is (a) 2dgh (b) dgha (ii) (c) 2dgha (d) dgha

The mass of a bucket containing water is 10kg. What is the work done in pulling up the bucket from a well of depth 10m if water is pouring out at a uniform rate from a hole in it and there is loss of 2kg of water from it while it reaches the top (g 10 msec). (a) 1000 J (b) 800 J (c) 900 J (d) 500 J

A rod of mass m and length is lying on a horizontal table. The work done in making it stand on one end will be (a) mgl (b) mgl 2 (c) mgl 4 (d) 2mgl

A metre stick, of mass 400g, is pivoted at one end displaced through an angle 60. The increase in its potential energy is 600,(a) 1 J (b) 10J (c) 100 J (d) 1000 J

Once a choice is made regarding zero potential energy reference state, the changes in potential energy (a) Are same (b) Are different (c) Depend strictly on the choice of the zero of potential energy (d) Become indeterminate

A uniform chain of length 2m is held on a smooth horizontal table so that half of it hangs over the edge. If it is released from rest, the velocity with which it leaves the table will be nearest to (a) 2 ms (b) 4 ms (c) 6 ms (d) 8 ms

Two stones each of mass 5kg fall on a wheel from a height of 10m. The wheel stirs 2kg water. The rise in of water would be (b) 1.2C temperature (a) 2.6C (c) 0.32C (d) 0.12C

A boy is sitting on a swing at a maximum height of 5m above the ground. When the swing passes through the mean position which is 2m above the ground its velocity is approximately. h2m B Th5m (a) 7.6 ms (b) 9.8 ms (c) 6.26 ms (d) None

If we throw a body upwards with velocity of 4 ms at what height its kinetic energy reduces to half of the initial value Take g 10 ms. (a) 4m (b) 2 m (c) 1 m (d) None

A 2kg block is dropped from a height of 0.4 m on a spring of force constant K 1960 Nm. The maximum compression of the spring is (a) 0.1 m (b) 0.2 m (c) 0.3 m (d) 0.4 m

A block of mass 2kg is released from A on the track tht is one quadrant of a circle of radius 1m. It slides down the track and reaches B with a speed of 4 ms and finally stops at C at a distance of 3m from B. The work done against the force of friction is (a) 10J A 2k (b) 20 J Im (c) 2 J (d) 6J

A stone projected vertically upwards from the ground 3h reaches a maximum height h. When it is at a height 4 the ratio of its kinetic and potential energies is (a) 34 (b) 13 (c) 43 (d) 31

A windpowered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed u, the electrical power output will be proportional to (a) v (b) (c) 13 (d) 14

A force applied by an engine of a train of mass 2.05 106 X kg changes its velocity from 5 ms to 25 ms in 5 minutes. The power of the engine is (a) 1.025 MW(b) 2.05 MW (c) 5 MW (d) 0.5 MW

From a water fall, water is falling at the rate of 100 kgs on the blades of turbine. If the height of the fall is 100m then the power delivered to the turbine is approximately equal to (a) 100 kW (b) 10 kW (c) 1 kW (d) 1000 kW

2.The displacement of the particle is given by y a bt ct dt4. The initial velocity and acceleration are

A bus weighing 100 quintals moves on a rough road with a constant speed of 72 kmh. The friction of the road is 9 of its weight and that of air is 1 of its weight. What is the power of the engine. Take g 10 ms. (a) 50 kW (b) 100 kW (c) 150 kW (d) 200 kW

A dam is situated at a height of 550 metre above sea level and supplies water to a power house which is at a height of 50 metre above sea level. 2000 kg of water passes through the turbines per second. The maximum electrical power output of the power house if the whole system were 80 efficient is (a) 8 MW (b) 10 MW (c) 12.5 MW (d) 16 MW

A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as (a) Poc 1 (b) Poct (c) Poc (d) Poc 132

n small balls each of mass m impinge elastically each second on a surface with velocity u. The force experienced by the surface will be (a) mnu (b) 2 mnu (c) 4 mnu 1 (d) mnu

A particle of mass m moving with horizontal speed 6 m sec. If m

A body of mass m moving with velocity v makes a head on collision with another body of mass 2m which is initially at rest. The loss of kinetic energy of the colliding body (mass m) is 1 (a) of its initial kinetic energy 1 (b) of its initial kinetic energy 8 (c) of its initial kinetic energy,1 (d) of its initial kinetic energy

A car moving on a straight road covers and third of the distance with 20 kmhr rest with 60 kmhr. The average speed is Let total distance travelled x km and total time taken

Consider the following statements Assertion (A) In an elastic collision of two billiard balls, the total kinetic energy is conserved during the short time of collision of the balls (i.e., when they are in contact) Energy spent against friction does not follow the law of conservation of energy of these statements. Reason (R) (a) Both A and R are

A car of mass 400kg and travelling at 72 kmhr crashes into a truck of mass 4000 kg and travelling at 9 kmhr, in the same direction. The car bounces back at a speed of 18 kmhr. The speed of the truck after the impact is (a) 9 kmhr (b) 18 kmhr (c) 27 kmhr (d) 36 kmhr

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is 2uM m (a) (b) 2um M (c) 2u 1 m M (d) 2u M m 1

A ball moving horizontally with speed u strikes the bob of a simple pendulum at rest. The mass of the bob is equal to that of the ball. If the collision is elastic the bob will rise to a height. (a) 1 g To m m (m) (b) 28 (c) 1 4g (d) 88

A moving body with a mass m, strikes a stationary body of mass m. The masses m, and m, should be in the ratio m so as to decrease the velocity of the first body 1.5 m times assuming a perfectly elastic impact. Then the ratio m m is 25 (b) 5 (c) 5 (d) 25

A moving mass of 8kg collides elastically with a stationary mass of 2 kg. If E be the initial kinetic energy of the mass, the kinetic energy left with it after collision will be (a) 0.80E (b) 0.64 E (c) 0.36 E (d) 0.08 E

A neutron travelling with a velocity v K.E. E collides perfectly elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by neutron is (a) A 41) (4) A (b) A A1, (a)(41) A

A neutron with 0.6 MeV kinetic energy directly collides with a stationary carbon nucleus (mass number 12). The kinetic energy of carbon nucleus after the collision is,(a) 1.7 MeV (b) 0.17 MeV (c) 17 MeV (d) zero

A body of mass m moving along a straight line collides with a body of mass nm which is also moving with a velocity ku in the same direction. If the first body comes to rest after the collision, then the velocity of second body after the collision would be nv (1nk) (1nk) v (c) n (a) nv (1nk) (b) (1 nk)v (d) n

Which one of the following statement does not hold good when two balls of masses m, m, undergo elastic collsion (a) When m, m, and m, at rest, after collision the ball of mass m, moves with four times the velocity m. (c) When m m, and m, at rest, there will be maximum transfer of kinetic energy. (d) When collision is oblique m at rest with m m,

Keeping the principle of conservation of momentum in mind which of the following collision diagram is not correct. (a)O M (c)o M M MIC M M j M .90 M (b)o M .....(d)o Mi M M M 90 M M

Three particles A, B and C of equal mass are moving with the same velocity v along the medians of an equilateral triangle. These particle collide at the centre G of triangle. After collision A becomes stationary, B retraces its path with velocity u then the magnitude and direction of velocity of C will be B (a) u and opposite to B (b) u in the

A ball B, of mass M moving northwards with velocity v collides elastically with another ball B of same mass but moving eastwards with the same velocity v. Which of the following statements will be true (a) B, comes to rest but B moves with velocity 2 v. (b) B, moves with velocity 2 v but B comes to rest. V (c) Both move with velocity in north east

The ratio of masses of two balls is 2 1 and before collision the ratio of their velocities is 1 2 in mutually opposite direction. After collision each ball moves in an opposite direction to its initial direction. If e ratio of speed of each ball before and after collision would be (2m)..... m UU 5 (1). 6 5 (a) times (b) Equal (c) Not related 6

A body of mass 3kg, moving with a speed of 4 ms, collides head on with a stationary body of mass 2kg. Their relative velocity of separation after the collision is 2 ms. Then (a) The coefficient of restitution is 0.5 (b) The impulse of the collision is 7.2 Ns (c) The loss of kinetic energy due to collision is 3.6J (d) The loss of kinetic energy due

A body falling from a height of 20m rebounds from hard floor. If it loses 20 energy in the impact, then coefficient of restitution is (a) 0.89 (b) 0.56 (c) 0.23 (d) 0.18

Which of the following is not a perfectly inelastic collision (a) Striking of two glass balls (b) A bullet striking a bag of sand (c) An electron captured by a proton (d) A man jumping onto a moving cart

A mass of 20kg moving with a speed of 10 ms collides with another stationary mass of 5 kg. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be (a) 600J (b) 800J (c) 1000 J (d) 1200 J

A neutron having mass of 1.67 1027 kg and moving at 108 ms collides with a deutron at rest and sticks to it. If the mass of the deutron is 3.34 1027 kg the speed of the combination is (a) 2.56 10 ms X (c) 3.33 107 ms (b) 2.98 x 105 ms (d) 5.01 x 10 ms

A ball moving with speed v hits another identical ball of rest. The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision is 1 (a) 8.S (b) 45 1 2S (c) (d) 1 S

A bullet of mass a is fired with velocity b in a large block of mass c. The final velocity of the system will be (a) C ac a ab ac (b) atc (ab)(a c) (d) b a (c) C

A particle of mass 1g having velocity 32 j has a glued impact with another particle of mass 2g velocity,as 46k. Velocity of the formed particle is (a) 5.6 ms (b) 0 (c) 6.4 ms (d) 4.6 ms

A body of mass 2kg is placed on a horizontal frictionless surface. It is connected to one end of a spring whose N force constant is 250. The other end of the spring is m joined with the wall. A particle of mass 0.15kg moving horizontally with speed v sticks to the body after collision. If it compresses the spring by 10cm, the velocity of the

A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embeded into it. The kinetic energy of the composite block will be 1 (a) myx m (mM) 1 (c) myx (Mm) M 1 (b) mv M (mM) 1 (d) Mx m (mM)

A mass of 10gm, moving horizontally with a velocity of 100 cmsec, strikes the bob of a pendulum and strikes to it. The mass of the bob is also 10 gm (see figure). The maximum height to which the system can be raised is (g 10 msec) (a) zero 10 gm ms 10 gm (b) 5 cm (c) 2.5 cm (d) 1.25 cm

A bag P (mass M) hangs by a long thread and a bullet (mass M) comes horizontally with velocity v and gets caught in the bag. Then for the combined (beg bullet) system the (a) Momentum is mvM M m (b) Kinetic energy (c) Momentum is mv 2 mv (M m) M (d) Kinetic energy is mV 2(M m)

A wooden block of mass M is suspended by a cord and is at rest. A bullet of mass m, moving with a velocity v pierces through the block and comes out with a velocity in the same direction. If there is no loss in kinetic 2 energy, then upto what height the block will rise,mv 2Mg mv (b) 8Mg (c) mv 4Mg mv (d) 2Mg

In a cubic unit cell with the planes (111), (202), (132) and (100). Calculate the inter planer distances for these planers if a=4.8A".

The color code of a resistance is given below Yellow Violet Brown Gold The values of resistance and tolerance, respectively, are (1) 470 52, 5 (3) 47 kn, 10 (2) 470 kn, 5 (4) 4.7 kn, 5

Find the torque about the origin when a force of 31 N acts on a particle whose position vector is 2km (1) 6k Nm (3) 61 Nm (2) 61 Nm (4) 61 Nm

A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27C. Its density is (R 8.3 J mol K) (1) 0.02 kgm (3) 0.2 kgm (2) 0.5 kgm (4) 0.1 kgm

Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is (1) isobaric (3) adiabatic (2) isothermal (4) isochoric

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of (1) 80 cm (2) 33 cm (4) 67 cm (3) 50 cm

A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is , then the angle of incidence is nearly equal to (1) (3) 2 2A (2) A 2 (4)

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth (1) 24 N (3) 32 N (2) 48 N (4) 30 N

An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 Am . The permeability of the material of the rod is ( (Ho 4 x 107 Tm A) (1) 2.4 x 107 Tm A (2) 2.4 x 104 Tm A (3) 8.0 x 105 Tm A (4) 2.4 x 105 Tm A

For transistor action, which of the following statements is correct (1) The base region must be very thin and lightly doped. (2) Base, emitter and collector regions should have same doping concentrations. (3) Base, emitter and collector regions should have same size. (4) Both emitter junction as well as the collector junction are forward biased.

Light with an average flux of 20 Wcm falls on a nonreflecting surface at normal incidence having surface area 20 cm. The energy received by the surface during time span of 1 minute is (1) 48 10 J (2) 10 10 J (3) 12 x 10 J (4) 24 x 10 J