The velocity of a body moving in a vertical circle of radius r is √7 g r at the lowest point of the circle. What is the ratio of maximum and minimum tension ?

Question

The velocity of a body moving in a vertical circle of radius r is √7 g r at the lowest point of the circle. What is the ratio of maximum and minimum tension ? (A) 4: 1 (B) √7: 1 (C) 3: 1 (D) 2: 1

Tardigrade Admin · Accepted Answer

Tension is maximum at the lowest point and minimum at the highest point. Tension at the lowest point,

T_{L} = m g + \frac{m v _{L}^{2}}{r} = m g + \frac{7 m g r}{r} = 8 m g (∵ v_{L} = 7 g r)

Tension at the highest point,

T_{H} = \frac{m v _{H}^{2}}{r} - m g = \frac{m ( v _{L}^{2} - 4 g r )}{r} - m g (∴ v_{L}^{2} - v_{H}^{2} = 4 g r)

= \frac{m ( 7 g r - 4 g r )}{r} - m g = 3 m g - m g = 2 m g

∴ \frac{T _{L}}{T _{H}} = \frac{4}{1}

or

\frac{T _{m a x}}{T _{m i n}} = \frac{4}{1}

Q. The velocity of a body moving in a vertical circle of radius $r$ is $7 g r$ at the lowest point of the circle. What is the ratio of maximum and minimum tension ?

4 : 1

$7 : 1$

3 : 1

2 : 1

Q. The velocity of a body moving in a vertical circle of radius r is 7gr​ at the lowest point of the circle. What is the ratio of maximum and minimum tension ?

4 : 1

7​:1

3 : 1

2 : 1

Q. The velocity of a body moving in a vertical circle of radius $r$ is $7 g r$ at the lowest point of the circle. What is the ratio of maximum and minimum tension ?

$7 : 1$