$A$ ball of mass $m$ is released from the top of a smooth movable wedge of mass $m$. When the ball collides with the floor,the velocity of the wedge is $v$. Then the maximum height attained by the ball after an elastic collision with the floor is: (Neglect any edge at the lower end of the wedge).

$A$ metallic block of mass $20 \ kg$ is dragged with a uniform velocity of $0.5 \ ms^{-1}$ on a horizontal table for $2.1 \ s$. The coefficient of kinetic friction between the block and the table is $0.10$. What will be the maximum possible rise in temperature of the metal block if the specific heat of the block is $0.1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$ (in $^{\circ} C$)? Assume $g = 10 \ ms^{-2}$ and a uniform rise in temperature throughout the whole block. [Ignore absorption of heat by the table]

Write the relation between the coefficient of static friction,kinetic friction,and rolling friction.

In which of the following graphs,the total change in momentum is zero?

$A$ car of mass $500\, kg$ is driven with acceleration $1\, m/s^2$ along a straight level road against a constant external resistance of $1000\, N$. When the velocity is $5\, m/s$,the rate at which the engine is working is .............. $kW$.

Statement $I :$ $A$ cyclist is moving on an unbanked road with a speed of $7 \, km/h$ and takes a sharp circular turn along a path of radius $2 \, m$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $(g = 9.8 \, m/s^2)$.
Statement $II :$ If the road is banked at an angle of $45^{\circ}$,the cyclist can cross the curve of $2 \, m$ radius with a speed of $18.5 \, km/h$ without slipping.