PHYSICS PROBLEMS Set 2

PHYSICS PROBLEMS: Set 2Problem 1: In the arrangement shown in fig. 1 pulleys X and Y are light and frictionless, their masse being 4 kg and 11.25 kg respectively while masses of blocks P, Q and R are 2m, m and M respectively. When the system is released from rest, downward accelerations of blocks Q and R relative to P are found to be 5 ms - 2 and 3 ms- 2 respectively. Calculate: (a) accelerations of blocks Q and R, relative to the ground and (b) mass of each block (g = 10 ms-2)Problem 2: In the arrangement shown in fig. 2 masses of the blocks X, Y and Z are 7.5 kg, 6 kg and 1 kg respectively. The pulley is a circular disc of mass 0.5 kg, radius 20 cm and thickness 1 cm. The rope between block X and pulley is horizontal and that between pulley and block Z is vertical. The pulley is free to rotate about its horizontal axis without friction and rope does not slip over the pulley. Neglecting friction between blocks Y and Z and, that between blocks and the floor, calculate resultant acceleration of block Z when the system is released. (g = 10 ms-2)Problem 3: In the arrangement shown in fig. 3, a wedge of mass m3 = 3.45 kg is placed on a smooth horizontal surface as shown. A light, flexible rope passes over a small and light pulley connected on its top edge. Two blocks of masses m1 = 1.3 kg and m2 = 1.5 kg are connected at the ends of the rope. The block m1 lies on smooth horizontal surface and m2 rests on inclined surface of the wedge. The base length of the wedge is 2 m and inclination is 370. The block m2 is initially near the top edge of the wedge. If the whole system is released from rest, calculate: (a) velocity of wedge when m2 reaches its bottom, (b) velocity of m2 at that instant and tension in the rope during motion of m2.All the surfaces are smooth. (g = 10 ms-2)Problem 4: Two blocks of mass m1 and m2 are attached at the ends of an ideal spring of force constant k and normal length lo. The system rests on smooth horizontal plane. The blocks are pulled apart by applying forces F1 and F2 respectively, as shown in fig. 4. Calculate maximum elongation of the spring.Problem 5: A uniform solid sphere of radius R = 22 cm is cut into two parts by a plane at a distance of 13.2 cm from the centre of the sphere as shown in fig. 5. Calculate the distance of centre of mass of heavier part from the centre O.Problem 6: A vehicle of mass m starts moving along a horizontal circle of radius R such that its speed varies with distance s covered by the vehicle as v = k, where k is a constant. Calculate: (a) tangential and normal force on vehicle as function of distance s, (b) distance s in terms of time t and (c) work done by the resultant force in first t seconds after the beginning of motion.Problem 7: A particle of mass m moves along a horizontal circle of radius R such that centripetal acceleration of particle varies with time as ac = kt2, where k is a constant. Calculate: (a) tangential force on the particle at time t, (b) total force on particle at time t, (c) power developed by total force at time t, and (d) average power developed by total force over first t second.Problem 8: Two identical blocks P and Q, each of mass m = 2 kg are connected to the ends of an ideal spring having a force constant k = 1000 N/m. This system is placed on a rough floor. The co-efficient of friction between blocks and floor is µ = 0.5. The block P is pressed towards right so that spring gets compressed. (a) Calculate initial minimum compression xo of spring such that block Q leaves contact with the wall when the system is released. (b) If initial compression of spring is x =2 xo, calculate the velocity of centre of mass of the system when block Q just leaves contact with the wall. (g = 10 ms-2)Problem 9: An ice cube of size 20 cm is floating in a tank of base area A = 50 cm x 50 cm partially filled with water. The density of water is 1000 kgm-3 and that of ice is 900kgm-3. Calculate increase in gravitational potential energy when ice melts completely. (g = 10 ms-2)Problem 10: A cubical block of wood of density 500 kg m-3 has side of 30 cm. It is floating in a rectangular tank partially filled with water of density 1000 kg m-3 and having base area A = 45 cm x 60 cm. Calculate work done to press the block so that it is just immersed in water. (g = 10 ms-2)