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)

increase by a factor of 4

Answer 2

$K \cdot E =\underset{ RI }{2}$
$\because$ From angular momentum conservation about centre.
$L \rightarrow$ constant
$I = mr$
$K \cdot E \cdot=\underset{2(\operatorname{tar})}{2,2} r =$
$K . E .=4 K . E .$
K.E. is increased by a factor of $4 .$