Question:
By keeping moment of inertia of a body constant, if we double the time period, then angular momentum of body
By keeping moment of inertia of a body constant, if we double the time period, then angular momentum of body
Updated On: Jul 19, 2024
- remains constant
- becomes half
- doubles
- quadruples
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The Correct Option is B
Solution and Explanation
We know that angular momentum of the body is given by
$L=I \omega$
or $L=I\times \frac{2 \pi}{\tau}$
or $L \propto \frac{1}{T}$
$\Rightarrow \frac{L_1}{L_2}=\frac{T_2}{T_1}$
$\frac{L}{L_2}=\frac{2T}{T} (As ,T_2=2T)$
so,$L_2=\frac{L}{2}$ Thus, on doubling the time period, angular momentum of body becomes half.
$L=I \omega$
or $L=I\times \frac{2 \pi}{\tau}$
or $L \propto \frac{1}{T}$
$\Rightarrow \frac{L_1}{L_2}=\frac{T_2}{T_1}$
$\frac{L}{L_2}=\frac{2T}{T} (As ,T_2=2T)$
so,$L_2=\frac{L}{2}$ Thus, on doubling the time period, angular momentum of body becomes half.
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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.