Q. A small mass attached to a string rotates on a frictionless table top (the string passes through a hole at the centre of the table). 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) Increase by a factor of 4
B) Decrease by a factor of 2
C) Remain constant
D) Increase by a factor of 2
Explanation
[Solution from source] The string tension acts towards the hole, so angular momentum L = mvr is conserved. KE = L²/(2mr²), so halving r makes KE four times larger. Saying it stays constant ignores the work done by the pulling force. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.