JEE Main202523 Jan 2025Morning ShiftPhysicsRotational MotionActual
A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30^ with the horizontal. The speed of the particle at the bottom of the plane is v₁ . If the angle of inclination is increased to 45^ while keeping L constant. Then the new speed of the sphere at the bottom of the plane is v₂ . The ratio v₁^2: v₂^2 is
Options
- A1: 2
- B1: 3
- C1: 3
- D1: 2
Correct answer
A. 1: 2
Step-by-step solution
using WET aligned & W _ g = k _ f - k _ i & Mg ~L = k _ f - k _ i aligned K.E. in pure rolling 1 2 mV _ cm ^2+ 1 2 I _ cm ^2 aligned & = 1 2 mV ^2+ 1 2 2 5 mR ^2 ~V ^2 R ^2 & 7 10 mV ^2 aligned mgL = 7 10 mV _ f ^2-0 aligned & V _ f ^2 & ( ~V ₁ ~V ₂ )^2= ₁ ₂ = 30^ 45^ = 1 2 aligned