Question

A particle is given an initial speed $u$ inside a smooth spherical shell of radius $r$ such that it is just able to complete the circle. Acceleration of the particle at point B is

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

Answer 1

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


We know that the critical velocity at the bottom is given by $u=\sqrt{5gr}$
$u^2=5gr$

Using conservation of energy
$\Delta P.E=\Delta K.E$
$-mgr=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$

$\therefore v^2=u^2-2gr=5gr-2gr=3gr$

Tangential acceleration at $B$ is
$a_t=g$ (downwards)

Centripetal acceleration at $B$ is
$a_c=\frac{v^2}{r}=3g$

$\therefore$ Total acceleration will be
$a=\sqrt{a_c^2+a_t^2}=g\sqrt{10}$

Hence option A is the correct answer