Question

A sphere of mass m is released from the height 4r above the ground level on a smooth trek shown in the figure. The track ends in the from of a circular are of radius r. Find the speed of the sphere when it reaches the point Q:

• A. $\sqrt{\frac{10gr}{7}}$
• B. $\sqrt{\frac{30gr}{5}}$
• C. $\sqrt{\frac{50gr}{6}}$
• D. $\sqrt{10gr}$

Answer 1

The correct option is B $\sqrt{\frac{30gr}{5}}$

Applying energy conservation from top most point to Q

( K.E + P.E )${}_i$ = ( K.E + P.E )${}_f$

$\frac{1}{2}m(o{)}^2+mg(4r)$ = $\frac{1}{2}m{v}^2+mg\left(r\right)$

=$0+4gr$ = $\frac{v^2}{2}+gr$

$v^2=6gr$

v = $\sqrt{6gr}$ or $\sqrt{\frac{30gr}{5}}$