$A$ spring is compressed between two blocks of masses $m_1$ and $m_2$ placed on a horizontal surface as shown in the figure. When the blocks are released,they have initial velocities $v_1$ and $v_2$ as shown. The blocks travel distances $x_1$ and $x_2$ respectively before coming to rest due to friction. The ratio $\left( \frac{x_1}{x_2} \right)$ is

$Assertion$: On a rainy day,it is difficult to drive a car or bus at high speed.
$Reason$: The value of the coefficient of friction is lowered due to the wetting of the surface.

$A$ uniform wooden stick of mass $1.6 \,kg$ and length $l$ rests in an inclined manner on a smooth, vertical wall of height $h$ < $l$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. Find the ratio $h/l$ and the frictional force $f$ at the bottom of the stick. $(g=10 \,m \,s^{-2})$

When the bomb $Q$ explodes,the trolley of mass $200 \, kg$ travels a distance of $36 \, m$ before coming to rest. What distance will the trolley of mass $300 \, kg$ travel before coming to rest (in $, m$)?

$A$ block $A$ of mass $m_1$ rests on a horizontal table. $A$ light string connected to it passes over a frictionless pulley at the edge of the table,and from its other end,another block $B$ of mass $m_2$ is suspended. The coefficient of kinetic friction between the block $A$ and the table is $\mu_k$. When the block $A$ is sliding on the table,the tension in the string is:

$A$ $0.5\, kg$ ball moving with a speed of $12\, m/s$ strikes a hard wall at an angle of $30^\circ$ with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for $0.25\, s$,the average force acting on the wall is ........... $N$.