After head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\,\,m/s$ along positive $x-$ axis and the other has a speed of $2\,\,m/s$ along negative $x$ axis. The original velocities of the balls are
$-2\,\,m/s\,\,$ and $\,\,+3\,\,m/s$
$+2\,\,m/s\,\,$ and $\,\,+3\,\,m/s$
$-3\,\,m/s\,\,$ and $\,\,+2\,\,m/s$
$+3\,\,m/s\,\,$ and $\,\,-2\,\,m/s$
Consider two carts, of masses $m$ and $2m$ , at rest on an air track. If you push both the carts for $3\,s$ exerting equal force on each, the kinetic energy of the light cart is
A basket and its contents have mass $M$. A monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3$ seconds. How fast is the basket rising at the end of the $3$ seconds? Neglect the mass of the pulley and the rope. (given : $g = 32ft/s^2$)
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 ball of mass $M$ falls from a height $h$ on a floor. If co-efficient of restitution is $e$, the height attained by the ball after two rebounds is
A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is