Question

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

• A. decrease by a factor of 2
• B. remain constant
• C. increase by a factor of 2
• D. increase by a factor of 4

Answer 1

Answer: (D)

According to law of conservation of angular momentum
$mvr=m{v}^{\prime }{r}^{\prime }$
$vr=v^{\prime }\left(\frac{r}{2}\right)$
$v^{\prime }=2v$...(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))
$K^{\prime }=4K$