Question

A small block is placed on the top of a smooth fixed sphere of radius $60$ cm. Block is slightly pushed so that it starts sliding of the sphere. Find the speed (in m/s) of the block when it leaves the sphere. $(g=10$ m/s${}^2$)

• A. $1$
• B. $\sqrt{2}$
• C. $2$
• D. $\sqrt{3}$

Answer 1

The correct option is C $2$

$mg$ $cos\theta =\frac{m{v}^2}{R}$ ......(i)

Mechanical energy conservation :

$\frac{1}{2}m{v}^2=mgR(1-\cos \theta )$ ......(ii)

From (i) and (ii) $\Rightarrow \cos \theta =\frac{2}{3}$

Now, $\Rightarrow v=\sqrt{Rg\cos \theta }=\sqrt{0.6\times 10\times \frac{2}{3}}=2m/s$