First slide

Rolling motion

Question

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB=D. The height h is equal to

Moderate

A

$\frac{3}{2} D$
B

$D$
C

$\frac{7}{5} D$
D

$\frac{5}{4} D$

Solution

As body is at rest initially, i.e., speed=0
At point A, speed=v As track is frictionless, so total mechanical energy will remain constant.
$∴ (T . M . E)_{i} = (T . M . E)_{f}$
$0 + m g h = \frac{1}{2} m v^{2} + 0 or h = \frac{v^{2}}{2 g}$
$For completing the vertical circle, v \geq \sqrt{5 g R}$
$∴ h = \frac{5 g R}{2 g} = \frac{5}{2} R = \frac{5}{4} D$

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