A particle $(\mathrm{m}=1\; \mathrm{kg})$ slides down a frictionless track $(AOC)$ starting from rest at a point $A$ (height $2\; \mathrm{m}$ ). After reaching $\mathrm{C}$, the particle continues to move freely in air as a projectile. When it reaching its highest point $P$ (height $1 \;\mathrm{m}$ ). the kinetic energy of the particle (in $\mathrm{J}$ ) is : (Figure drawn is schematic and not to scale; take $\left.g=10 \;\mathrm{ms}^{-2}\right)$
$8$
$10$
$15$
$13$
A small ball falling vertically downward with constant velocity $4m/s$ strikes elastically $a$ massive inclined cart moving with velocity $4m/s$ horizontally as shown. The velocity of the rebound of the ball is
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls ? (i.e. when they are in contact)
$(a)$ Kinetic energy.
$(b)$ Total linear momentum.
Give reason for your answer in each case.
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 $h$. Choose the correct statement related to the wedge $M$
A wire, which passes through the hole is a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is
A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.