Question

A mass is tied to a string and swung in a horizontal circle with a constant angular speed. show answer No Attempt If this speed is doubled, what happens to the tension in the string?

Answer 1

Answer:

The tension in the string is quadrupled i.e. increased by a factor of 4.

Explanation:

The tension in the string is the centripetal force. This force is given by

$F = \dfrac{mv^2}{r}$

m is the mass, v is the velocity and r is the radius.

It follows that $F \propto v^2$, provided m and r are constant.

When v is doubled, the new force, $F_1$, is

$F_1 = \dfrac{m(2v)^2}{r} = \dfrac{4mv^2}{r} = 4\dfrac{mv^2}{r} = 4F$

Hence, the tension in the string is quadrupled.