$A$ 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 $cc$)

$A$ small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has a coefficient of friction $\mu$. The ball comes to a stop at $C$ after traveling a distance $L$. The value of $L$ is:

Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same and the compression of the spring is $x_0$. The spring constant $k$ will be

$A$ baseball having mass of $0.4 \ kg$ is thrown such that one of the forces acting on it varies with time as shown in the first graph. Also,the velocity of the ball is in the same direction as the force. The velocity varies with time as shown in the second graph. Choose the incorrect option (up to $0.3 \ s$).

Statement $-1$: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement $-2$: Principle of conservation of momentum holds true for all kinds of collisions.

In the case of circular motion of a body,if a tangential force also acts on the body in addition to a centripetal force,then the work done: