A block of mass m is placed at the lowest point of a smooth vertical track of radius R . In this position, the block is given a horizontal velocity u such that the block is just able to perform a complete vertical circular motion. The acceleration of block, when its velocity is vertical is

Step-by-step solution

The initial velocity of the block to undergo a complete vertical circular motion is u = 5 g R Let us assume that the speed of the block when it is moving in the vertical direction is v , then using conservation of mechanical energy we get 1 2 m 5 g R 2 = 1 2 m v 2 + m g R ⇒ v 2 = 3 g R The tangential and centripetal accelerations of the block are a t = g   ↓ and a c = 3 g   ← a net = a c 2 + a t 2 = g 10