Question

A particle is given an initial speed $u$ inside a smooth spherical shell of radius $R=1\text{m}$, so that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical, is

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

Answer 1

The correct option is A $g\sqrt{10}$

As per the question, the situation of the block is shown



As we know that the minimum velocity required to complete the circle is
$u^2=5gR$
$\therefore$ Applying the concept of energy conservation between $A$ and $B$, we get
$v^2=u^2-2gR$
$\Rightarrow v^2=5gR-2gR=3gR$

Now, tangential acceleration at $B$ is
$a_t=g$ (downwards)
and, centripetal acceleration at $B$ is
$a_c=\frac{v^2}{R}=\frac{3gR}{R}=3g$
$\therefore$ Net acceleration at $B$ will be
$a_n=\sqrt{a_c^2+a_t^2}=\sqrt{(3g{)}^2+(g{)}^2}=g\sqrt{10}$