devarshi-dt-logo

Question:

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is (are) correct?

Cylinder P has larger linear acceleration than cylinder Q.

Both cylinders reach the ground with same translational kinetic energy.

Both cylinders P and Q reach the ground at the same time.

Cylinder Q reaches the ground with larger angular speed.

Solution:

Acceleration is a = gsinθ/(1 + I/MR²)
aP = gsinθ/(1 + MR²/R²) = g/2
aQ = gsinθ (as I of Q is similar to 0)
ωp = √(2g/2l/R)
ωQ = √(2gl/R)
Thus ωp > ωQ