Question

2. A small box of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the box makes an angle of 30° with the vertical. The box is released from the position. (a) What is the force exerted by the sphere on the box just after the release? (b) Find the distance travelled by the box before it leaves contact with the sphere. 3. A particle is suspended from a fixed point by a string of length 5 m. It is projected from the equilibrium position with such a velocity that the string slackens after the particle has reached a height 8 m above the lowest point. Find the velocity of the particle just before the string slackens. Find also to what height the particle can rise further. 4. A heavy particle hanging from a fixed point by a light inextensible string of length is projected horizontally with speed vgl. Find the speed of the particle and the inclination of the string to the vertical at the instant when the tension in the string equals the weight of the particle. 5. A ball is attached to a horizontal cord of length I whose other end is fixed. (a) If the ball is released, what will be its speed at the lowest point of its path? (b) A peg is located a distance h directly below the point of attachment of the cord. If h 0.751, what will be the speed of the ball when it reaches the top of its circular path about the peg? A smooth sphere of radius R is moving in a straight line with an acceleration a. A particle is released from the top of the sphere from rest. Find the speed of the particle when it is at an angular position θ from the initial position relative to the sphere 6.

Answer 1