Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 2: Exercise-2

A weightless ladder $20\mathrm{ft}$. long rests against a frictionless wall at an angle of $60°$ from the horizontal. A $150$ pound man is $4\mathrm{ft}$ from the bottom of the ladder. A horizontal force is needed to keep it from slipping. Choose the correct magnitude of force from the following :

$ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{\mathit{B}\mathit{C}}, I_{\mathit{C}\mathit{A}}$ are the moments of inertia of the plate about $AB, BC,CA$ respectively. Which one of the following relations is correct?

Assertion: A sphere of mass $m$ moving with speed $u$ undergoes a perfectly elastic head-on collision with another sphere of heavier mass $M$ at rest $(M>m)$, then the direction of the velocity of the sphere of mass $m$ is reversed due to collision [no external force acts on a system of two spheres]

Reason: During a collision of spheres of unequal masses, the heavier mass exerts more force on lighter mass in comparison to the force which lighter mass exerts on heavier mass.

Assertion: If the mass of the colliding particles remains constant, then the linear velocity of the individual particles change during collision along common normal direction.

Reason: A pair of equal and opposite impulses act along common normal direction.

Assertion : A shell at rest, explodes. The centre of mass of fragments moves along a straight path.

Reason : In explosion the linear momentum of the system remains always conserved.

Assertion : Position of centre of mass is independent of the reference frame:
Reason: Centre of mass is same for all bodies.

Assertion : The position of centre of mass of a body does not depend upon shape and size of the
body. Reason : Centre of mass of a body lies always at the centre of the body.

Assertion : When a body dropped from a height explodes in mid air, its centre of mass keeps moving in vertically downward direction.

Reason : Explosion occur under internal forces only. External force is zero.