First slide

Vertical circular motion

Question

A stone is rotated in a vertical circle. Speed at bottommost point is $\sqrt{8 g R}$ where R is the radius of circle. The ratio of tension at the top and the bottom is

Moderate

A

1 : 2
B

1 : 3
C

2: 3
D

1 : 4

Solution

$T = \frac{m u^{2}}{R} + m g \cos θ; v^{2} = u^{2} - 2 g h$
$T_{top} = 3 m g and T_{bottom} = 9 m g$
Therefore, the ratio $\frac{T_{top}}{T_{bottom}} = \frac{3 m g}{9 m g} = \frac{1}{3}$

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