Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions, stick together after collision. If the balls were initially moving with a velocity of $45\sqrt 2 \,m{s^{ - 1}}$ each, the velocity of their combined mass after collision is .................. $\mathrm{m} / \mathrm{s}^{-1}$

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Suppose the particle when reaches the horizontal surfaces, its velocity with respect to ground is $v_1$ and that of wedge is $v_2$. Choose the correct statement(s)

Write the principle of conservation of mechanical energy for conservative force.

A particle of mass m moving with velocity ${V_0}$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be

In the figure shown, a particle is released from the position $A$ on a smooth track. When the particle reaches at $B$, then normal reaction on it by the track is .........

$A$ $4$ -kilogram disk slides over level ice toward the east at a velocity of $1$ meter per second, as shown. The disk strikes a post and rebounds toward the north at the same speed. The change in the magnitude of the eastward component of the momentum of the disk is ............. $\mathrm{kg}$ $ \cdot $ $\mathrm{m}/ \mathrm{s}$