First slide

Vertical circular motion

Question

The velocity of a body revolving in a vertical circle of radius ‘r’ at the lowest point is √(7gr) . The ratio of maximum to minimum tensions in the string is

Moderate

A

8 : 1
B

4 : 1
C

√7 : 1
D

1 : √7

Solution

$\large {T_{\max }} = \frac{{m{v^2}}}{r} + mg = 8mg$
Conserving energy - 1/2 mu² +mg .2r = 1/2 mV²
⇒ mu² / r = m(√(7gr))² / r - 4 mg = 3 mg
.: T_min + mg = mu²/r ⇒ T_min = 3 mg - mg = 2 mg
.: T_max / T_min = 8 mg / 2mg = 4 / 1

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