PHYSICS PROBLEMS Set 1

PHYSICS PROBLEMS: Set 1Problem 1: Two inclined planes XY and YZ are inclined at 300 and 600 with the horizontal, respectively. These planes intersect each other at Y as shown in Fig.1. A particle is projected from point A with a velocity u (= 10 m/s) along a direction perpendicular to plane XY. If the particle strikes plane YZ perpendicularly at point B, calculate: (a) velocity with which particle strikes the plane YZ, (b) time of flight, (c) vertical height h of point A from Y, (d) maximum height from Y, attained by the particle and (e) distance AB. (g = 10 m/s2)Problem 2: A particle is moving along a vertical circle of radius R = 2 m with a constant speed of 3.14m/s as shown in Fig. 2. The straight line XYZ is horizontal and passes through the centre of the circle. A shell is fired from point X at the instant when particle is at Z. If distance XY is 20 m and shell collides with the particle at Y, calculate (a) smallest possible value of the angle α of projection, (b) corresponding velocity of projection. Problem 3: A particle is projected from point X on the ground with 5 m/s at angle θ = tan-1 (0.5). It strikes at a point A on a fixed smooth plane YZ, inclined at an angle of 370 with the horizontal. See fig. 3. If the particle does not rebound, calculate (a) the height of point A, (b) maximum height from the ground to which the particle rises. Given XY = 10/3 m and g = 10 m/s2.Problem 4: Two identical shells are fired from a point on the ground with same muzzle velocity at angles of elevation 450 and tan-1 3 towards the top of a cliff, 20 m away from the point of firing. If both the shells reach the top simultaneously, calculate(a) muzzle velocity, (b) height of the cliff and (c) time interval between two firings.If just before striking the top of cliff the two shells get stuck together, considering elastic collision of combined body with the top, calculate(d) maximum height reached by the combined body. g = 10 m/s2Problem 5: A shell of mass m = 0.700 kg is fired from ground with a velocity 20 m/s. At highest point of is trajectory, it collides in-elastically with a ball of mass 0.300 kg, suspended by a flexible thread of length 1.40 m. If thread deviates through an angle of 1200, calculate(a) angle of projection of the shell, (b) maximum height of combined body from ground and (iii) distance between point of suspension of ball and point of projection of the shell. g = 10 m/s2Problem 6: Two small particles X and Y having masses 0.5 kg each and charge qX = µC and qY = +100 µC respectively, are connected at the ends of a non-conducting, flexible & inextensible string of length 0.5 m. The particle X is fixed and the particle Y is whirled in a vertical circle with centre at X. If a vertically upward electric field of strength E = 1.1 × 105 N/C exists in the space, calculate minimum velocity of particle Y, required at highest point so that it just completes the circle. g = 10 m/s2Problem 7: A small sphere of mass 0.5 kg carrying a positive charge of 110 µC is connected with a light, flexible and inextensible string of length 60 cm and whirled in a vertical circle. If a vertically upward electric field of strength 105 N/C exists in the space, calculate minimum velocity of sphere required at highest point so that it just completes the circle. g = 10 m/s2Problem 8: Two blocks X and Y of masses 1 kg and 2 kg respectively are connected by a light string, passing over a light frictionless pulley. Both the blocks are in contact with the horizontal floor at t = 0 and the pulley is held such that string remains just taut. At t = 0, a force F = 20 t N starts acting on the pulley along vertically upward direction, as shown in Fig. 4. Calculate the velocity of X when Y loses contact with the floor. g = 10 m/s2Problem 9: In the arrangement shown in Fig. 5 pulleys are small, light and frictionless, threads are inextensible and mass of blocks X, Y and Z is mx = 5 kg, my = 4 kg and mz = 2.5 kg respectively. Coefficient of friction for both the planes is µ = 0.50. Calculate acceleration of each block when system is released from rest. g = 10 m/s2Problem 10: A block resting over a horizontal floor has a symmetric track XYZ, as shown in Fig. 6. The mass of the block is m1 = 3.12 kg. The length XY = YZ = 1 m. A block of mass m2 = 2 kg is put on the track at X and system is released from rest. Neglecting friction and impact at Y, calculate the time period of horizontal oscillations performed by the block of mass m1.