Question

A small mass attached to a string rotates on a frictionless table top as shown in Fig. 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. `(1)/(4)mv_(0)^(2)`
B. `2mv_(0)^(2)`
C. `(1)/(2)mv_(0)^(2)`
D. `mv_(0)^(2)`

Answer 1

Correct Answer - B
Angular momentum remains constant because the torque of tension is zero.
`:. L_(i) = L_(f) or mv_(0) R = mv (R )/(2) or v = 2v_(0)`
`:.` final kinetic energy `K_(f) = (1)/(2)m (2v_(0))^(2)`
`= 2mv_(0)^(2)`