An object of mass $M$ is at rest on smooth horizontal surface. Objects of different masses collide head on elastically to the object of mass $M$ . All colliding objects are having fixed same kinetic energy and in each case mass $M$ is supposed to be at rest initially. In this experiment the kinetic energy transferred to stationary mass $(M)$ depend on linear momentum of incoming colliding mass then energy transferred to $M$ in a collision is
first increases then decreases with linear momentum
first decreases then increases with linear momentum
always decreases with linear momentum
always increases with linear momentnm
A dumbbell consisting of two masses $m$ each, connected by a light rigid rod of length $l$, falls on two pads of equal height, one steel and the other brass through a height $h$. The coefficient of restitution are $e_1$ and $e_2$ ($e_1 < e_2$). To what maximum height will the centre of mass of the dumbbell rise after bouncing of the pads?
$Assertion$ : In an elastic collision of two billiard balls, the total kinetic energy is conserved during the short time of oscillation of the balls (i.e., when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.
Which of the following statement is true?
In the figure shown, the two identical balls of mass $M$ and radius $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass $M$ and radius $R/2$, is coming down vertically and has a velocity $= v_0$ when it simultaneously hits the two balls and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to
Two cars, both of mass $m$ , collide and stick together. Prior to the collision, one car had been traveling north at speed $2v$ , while the second was traveling at speed $v$ at an angle $\phi $ south of east (as indicated in the figure). The magnitude of the velocity of the two car system immediately after the collision is