Question

A Block is released from rest at the top of an inclined plane which later curves into a circular track of radius r as shown. Find the minimum height h from where it should be released so that it is able to complete the circle.

• A. 5r
• B.
• C.
• D. 2r

Answer 1

The correct option is B

Let the P.E at the ground = 0.

Let the velocity of the block at highest point of circular track = 'v'

At the forces acting on block are gravity and normal but normal reaction does no work and friction is absent, so we conserve energy

$K_i+V_i=K_f+V_f$

0 + mgh = $\frac{1}{2}m{v}^2$ + mg (2r) ....(i)

At the highest point, the centripetal force is provided by N and mg,

From Newton's Law,

N + mg = $\frac{m{v}^2}{r}$ for min, velocity,N = 0

mg = $\frac{m{v}^2}{r}\Rightarrow =\sqrt{gr}$

Using eqn.(1)

mgh = $\frac{1}{2}mgr+mg\left(2r\right)$

$h=\frac{5r}{2}$