Two solid cylinders and of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder has most of its mass concentrated near its surface, while has most of its mass concentrated near the axis. W

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? [2012]

Smart Achievers · Accepted Answer

(4)

As we know, acceleration of the center of mass of a cylinder rolling down an inclined plane

$a_{c} = \frac{g \sin θ}{1 + \frac{I}{M R^{2}}}$

In case of P the mass is concentrated away from the axis,

$So I_{P} > I_{Q}$

$∴$ $a_{P} < a_{Q} \Rightarrow v_{P} < v_{Q} \Rightarrow ω_{P} < ω_{Q}$

Solution

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

2 Cylinder P has larger linear acceleration than cylinder Q.

3 Both cylinders reach the ground with same translational kinetic energy.

4 Cylinder Q reaches the ground with larger angular speed.

Want Us to Email you About Special Offers & Updates?