NEET2011PhysicsRotational MotionActual
A small mass attached to a string rotates on frictionless table top as shown. If the tension is 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
Options
- Aremain constant
- Bincrease by a factor of 2
- Cincrease by a factor of 4
- Ddecrease by a factor of 2
Correct answer
C. increase by a factor of 4
Step-by-step solution
From the law of conservation of angular momentum So, aligned m v r & =m v^ r 2 y^ & =2 y k₁ k₂ & = 1 2 m v^2 1 2 m v^2 k₁ k₂ & = y^2 v^ 2 & = y^2 (2 v)^2 k₁ k₂ & = 1 4 k₁ & = 1 4 k₂ k₂ & =4 k₁ aligned