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?

• A. Both cylinders P and Q reach the ground at the same time
• B. Cylinder P has larger linear acceleration than cylinder Q
• C. Both cylinders reach the ground with same translational kinetic energy
• D. Cylinder Q reaches the ground with larger angular speed

Answer 1

Answer: (D)

Cylinder Q reaches the ground with larger angular speed

Answer 2

$Ip > Iq$
In case of pure rolling, $a=\frac{g sin ?}{1+I/mR^2}$
$a_Q > a_P$ as its moment of inertia is less. Therefore, Q reaches first with more linear speed and more translational kinetic energy.
Further, $?=\frac{V}{R}$ or $??v$
$\therefore ?_Q > ?_P$ as $v_P > v_Q$