Question

A 2 kg ball on a string is rotated about a circle of radius 10m. The maximum tension allowed in the string is 50N. What is the maximum speed of the ball (g = 10 ms-2)

Answer 1

Given:

A 2 kg ball on a string is rotated about a circle of radius 10m. The maximum tension allowed in the string is 50N.

To find:

Maximum speed of the ball ?

Calculation:

When an object is rotated in a vertical circle , the string has max tension at the lowest position.

Now , let max velocity be v :

According to FBD of ball (refer to diagram):

$\therefore \: T - mg = \dfrac{m {v}^{2} }{r}$

$\implies \: 50 - (2 \times 10) = \dfrac{2 {v}^{2} }{10}$

$\implies \: 50 - 20 = \dfrac{2 {v}^{2} }{10}$

$\implies \: 30 = \dfrac{ {v}^{2} }{5}$

$\implies \: {v}^{2} = 150$

$\implies \: v = \sqrt{150}$

$\implies \: v = 12.24 \: m {s}^{ - 1}$

So, maximum allowable speed for the ball is 12.24 m/s.