Question

The maximum and minimum tensions in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3. Then its velocity is

Options

• `sqrt(98)` m/s

• 7 m/s

• `sqrt(490)` m/s

• `sqrt(4.9)`

Answer 1

`sqrt(98)` m/s

Explanation:

In this problem, it is assumed that, while travelling in a vertical loop, the particle's speed remains constant.

Tension at lowest point, T_max = `(mv^2)/r + mg`

Tension at height point, T_min = `(mv^2)/r - mg`

∴ `(T_(max))/(T_(min)) = (((mv^2)/r + mg))/(((mv^2)/r - mg)) = 5/3`

`(3mv^2)/r + 3 mg = (5 mv^2)/r - 5 mg`

∴ 3v² + 3 rg = 5v² – 5 rg

∴ 2v² = 8 rg

∴ v = `sqrt(4 gr) = sqrt(4 xx 9.8 xx 2.5) = sqrt(98)` m/s