Question

A particle is given an initial speed $u$ inside a smooth spherical shell of radius $R$ 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. $g\sqrt{6}$

Answer 1

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

Let, the velocity at highest point be v then

$m{v}^2/r=mg\frac{m{u}^2}{2}=2\times mgR+\frac{m{v}^2}{2}$

$\Rightarrow u=\sqrt{5Rg}\frac{m{x}^2}{2}=\frac{m{u}^2}{2}-mgR$

Net acceleration at the point, when velocity is vertical is:

$a=\sqrt{{\left(\frac{m{x}^2}{2}\right)}^2+g^2}=\sqrt{10\times g}$

$=g\sqrt{10}$