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?
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?
Updated On: Jun 14, 2022
- Both cylinders P and Q reach the ground at the same time
- Cylinder P has larger linear acceleration than cylinder Q
- Both cylinders reach the ground with same translational kinetic energy
- Cylinder Q reaches the ground with larger angular speed
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The Correct Option is D
Solution and Explanation
$Ip > Iq$
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 $v_P > v_Q$
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 $v_P > v_Q$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.