$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

Two statements are given below. Select the option that correctly explains both statements.
Statement-$1$: In a perfectly elastic collision between two particles moving in the same direction,they do not lose all their energy.
Statement-$2$: The principle of conservation of momentum is valid for all types of collisions.

Starting from rest on her swing at initial height $h_0$ above the ground,Saina swings forward. At the lowest point of her motion,she grabs her bag that lies on the ground. Saina continues swinging forward to reach maximum height $h_1$. She then swings backward and when reaching the lowest point of motion again,she simply lets go of the bag,which falls freely. Saina's backward swing then reaches maximum height $h_2$. Neglecting air resistance,how are the three heights related?

In the diagram shown,there is no friction at any contact surface. Initially,the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be $K$.

$A$ small bob $A$ of mass $m$ is attached to a massless rigid rod of length $1 \ m$ pivoted at point $P$ and kept at an angle of $60^{\circ}$ with the vertical as shown in the figure. At a distance of $1 \ m$ below point $P$, an identical bob $B$ is kept at rest on a smooth horizontal surface that extends to a circular track of radius $R$ as shown in the figure. If bob $B$ just manages to complete the circular path of radius $R$ up to a point $Q$ after being hit elastically by bob $A$, then the radius $R$ is . . . . . . $m$.

$A$ car of mass $1000 \ kg$ has a motor of efficiency $20 \%$. If burning of one litre of petrol supplies $6 \times 10^7 \ J$ of energy,the amount of petrol used in accelerating the car from rest to $43.2 \ km \ h^{-1}$ is (in $cc$)