Question

A ball of mass 'm' is left at the top of an inclined plane of heght 'h' . At the foot of the plane, if the ball has to complete a vertical circle of radius R what is the least value of h ?

• A. $\frac{5}{2}R$
• B. $\frac{5}{3}R$
• C. $\frac{2}{3}R$
• D. $\frac{3}{4}R$

Answer 1

The correct option is A

$\frac{5}{2}R$

In order to complete the vertical circle, the ball should have a speed of $\sqrt{5Rg}$ at the foot of the plane.
$\therefore$ minimum K.E. at the foot $=\frac{5}{2}mRg$
P.E at the starting point =mgh
according to law of conservation of energy
$mgh=\frac{5}{2}mRg$
$\therefore h=\frac{5}{2}R$