Question

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

• A. $g$
• B. $3g$
• C. $g\sqrt{10}$
• D. $2\sqrt{2}g$

Answer 1

Answer: (C)

The initial velocity of the block to undergo a complete vertical circular motion is $u=\sqrt{5gR}$

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
$\frac{1}{2}m{\left(\sqrt{5gR}\right)}^2=\frac{1}{2}m{v}^2+mgR$
$\Rightarrow v^2=\sqrt{3gR}$
The tangential and centripetal accelerations of the block are
$a_t=g\left(\downarrow \right)$ and $a_c=3g\left(\leftarrow \right)$
$a_{net}=\sqrt{a_c^2+a_t^2}=g\sqrt{10}$