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  4. A ball of mass 0.25 kg attached to the ends of a string of length 1.96 m is rotating in a horizontal circle. The string will break, if tension is more than 25 N. What is the maximum velocity with which the ball can be rotated?

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Q. A ball of mass $0.25\, kg$ attached to the ends of a string of length $1.96\, m$ is rotating in a horizontal circle. The string will break, if tension is more than $25\, N$. What is the maximum velocity with which the ball can be rotated?

Uttarkhand PMTUttarkhand PMT 2004

Solution:

Given: $m=0.25\, kg , l=1.96\, m$
and $t=25 \,N$
Centrifugal force (tension) in the string is given by
$F=\frac{m v^{2}}{r} $
$\Rightarrow v^{2}=\frac{F r}{m} $
$\Rightarrow v^{2}=\frac{25 \times 1.96}{0.25}=196$
$\Rightarrow v=\sqrt{196}=14\, m / s$