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  4. A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 , the kinetic energy of the mass will

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Q. A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of $2$ , the kinetic energy of the mass willPhysics Question Image

AIPMTAIPMT 2011System of Particles and Rotational Motion

Solution:

According to law of conservation of angular momentum
$m v r=m v^{\prime} r^{\prime}$
$v r=v^{\prime}\left(\frac{r}{2}\right)$
$v^{\prime}=2 v$...(i)
$\therefore \frac{K}{K^{\prime}}=\frac{\frac{1}{2} m v^{2}}{\frac{1}{2} m v^{\prime 2}}=\left(\frac{v}{v^{\prime}}\right)^{2}$
or $\frac{K^{\prime}}{K} =\left(\frac{v^{\prime}}{v}\right)^{2}=(2)^{2} $(Using (i))
$K^{\prime} =4 K$