Consider a spherical object with radius R = 20 cm and mass M = 3 kg. A. If it is hollow, what is the moment of inertia (in kg . m ) of this object about an axis running through its center?B. If the object is solid what is the moment of inertia (in kg . m ) of this object about an axis running through its center?For questions A and B, assume the axis of rotation is perpendicular to the plane of the drawing and passes through point P. A. Calculate the moment of inertia (in kg - m2) of the \"opentriangle\" shown in the figure. Each side is 40 cm long, the total mass of the object is 500 g. Round to the nearest second decimal. B. If we bend one of the legs of this \"open-triangle\" (see figure), is the moment of inertia different from the one you found in part A? P a. Yes b. No c. Impossible to determine with the given information C. Taking the open-triangle, but changing the axis of rotation to align along one of (P the rods as shown in the figure, how does the moment of inertia compare to part : A? a) Increases b} Decreases c) Doesn't change d} Impossible to determine with the given information. D. With the object rotating about the new axis shown in the figure for Part C, calculate the new moment of inertia (in kg . m2). Round to the nearest second decimal.Problem 4 (Around a merry-go-round) A horizontal platform in the shape of a circular disk rotates freely in a horizontal plane about a frictionless, vertical axis through the center of the disk. The platform has a mass M = 100 kg and a radius R = 1.9 111. Two studentsJr whose masses are each m = 54 kg {treat them each as a point mass), are located on the disk at radius r = 1.6 In and r' = 0.9 m as shown in the figure. A. What is the total moment of inertia of the system? Provide your answer in kg - m2. B. The two children now move to the center of the disk, what is the total moment of inertia of the system? Provide your answer in kg - m2 . A. A S g beetle sits on the left end of a 30 cm plank whose pivot 'Is located at its center. Where on the plank should we place a 10 g grasshopper to balance it? (Report the distance as measured from the left end of the plank and use cm.) .I' 9' 1. ~. 30 cm B. Now assume we place the grasshopper on the right end of the plank. Where should the pivot be for the plank to be balanced? [Report the distance as measured from the left end of the plank and use cm.) A 75 kg man stands on his toes by exerting an upward force through the Achilles tendon, as shown below. For the questions below, you can assume that one foot supports hoif the man's weight and all torques are measured with respect to the pivot (indicated by a black circle}. Use 9 = 10 Infsz. P; is the tension on the Achilles Tendon acting on the heel. The pivot is the point of contact between the foot and the rest of the body, so there is a contact force on the foot at this point which we call FF. (Note that we ignore the weight of the foot itself.) A. What is the magnitude of the normal force in Newtons? (Hint: the entire body is not moving.) B. What is the torque due to the normal force about the pivot? Give y0u answer in N - m and include a negative Sign if needed. C. What force [in N) must the Achilles Tendon exert on the heel to keep the foot in static equilibrium? D. What is the magnitude of the force on the pivot? (Hint: not only the torques cancel out.)We can estimate the tension on the bicep muscle while lifting a weight with our hand. In this exercise, the lower arm pivots about the elbow (assumed xed}, while the bicep itself is attached to the lower arm 4- cm awayr from the elbow (see drawings below). The weight (W) has a mass of 10 kg and is assumed to be a point mass for simplicityf which exerting a force 15" \"h\" on the arm. The lower arm itself is modeled as a uniform rod with mass 3 kg and length 26 cm (from O to the center ofthe object}. For all questions below, torques are measured relative to the origin {0} and counterclockwise rotations are positive. A. What is the moment of inertia of the weight about an axis running through the origin (0}? Use units of kg - m2 and round to the rst decimal place. Assume the weight is 26 cm away from the origin 0. B. What is the moment of inertia of the lower arm about the same axis as in question A? Use units of kg . m and round to the nearest second decimal place.C. What is the total moment of inertia of the (lower arm + sphere) system about the same axis as question B? Use units of kg m2 and round to the nearest second decimal place. D. Now, assume we want to brieflyr give the weight an angular acceleration of 10 rad/32 directed counterclockwise. What is the tension (in Newtons) on the bicep required to accomplish this? (ignore the fact that the lower arm will rotate, changing its angles with the forces; picture this as a very short acceleration burst, so that we can assume the forces always act as in the diagram.)