Question:
A cubical block of side a moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is
A cubical block of side a moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is
Updated On: Jun 14, 2022
- $3v/4a$
- $3v/2a$
- $\sqrt3/\sqrt2a$
- Zero
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The Correct Option is A
Solution and Explanation
$r^2=\frac{a^2}{2}$
Net torque about O is zero.
Therefore, angular momentum (L) about O will be conserved,
or $L_i=L_f$
$Mv\bigg(\frac{a}{2}\bigg)=I_0?=(I_{cm}+Mr^2)?$
$=\biggl\{\bigg(\frac{Ma^2}{6}\bigg)+M\bigg(\frac{a^2}{2}\bigg)\biggl\}?$
$=\frac{2}{3}Ma^2?$
$?=\frac{3v}{4a}$
Net torque about O is zero.
Therefore, angular momentum (L) about O will be conserved,
or $L_i=L_f$
$Mv\bigg(\frac{a}{2}\bigg)=I_0?=(I_{cm}+Mr^2)?$
$=\biggl\{\bigg(\frac{Ma^2}{6}\bigg)+M\bigg(\frac{a^2}{2}\bigg)\biggl\}?$
$=\frac{2}{3}Ma^2?$
$?=\frac{3v}{4a}$
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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.