A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$
$7.2$
$3.6$
$120$
$1200$
Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2 m$ at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body $A$ is
$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
A container of mass $m$ is pulled by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$ . Initially the spring is in its natural length. Velocity of the container at the instant when compression in spring is maximum for the first time
Answer carefully, with reasons :
$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?
$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?
$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?
$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?
(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).
A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is