Two masses $m_1 = 5 \ kg$ and $m_2 = 10 \ kg$,connected by an inextensible string over a frictionless pulley,are arranged as shown in the figure. The coefficient of friction of the horizontal surface is $0.15$. The minimum mass $m$ that should be placed on top of $m_2$ to stop the motion is ........ $kg$. (in $.3$)

$A$ cubical box of side $a$ sitting on a rough table-top is pushed horizontally with a gradually increasing force until the box moves. If the force is applied at a height from the table top which is greater than a critical height $H$,the box topples first. If it is applied at a height less than $H$,the box starts sliding first. Then,the coefficient of friction between the box and the table top is

$A$ body of mass $2 \ kg$ is initially at rest. It moves on a table under the influence of a horizontal force of $7 \ N$. If the coefficient of kinetic friction is $0.1$,then the work done by the applied force and the work done by the frictional force in $10 \ s$ are respectively:

$A$ $0.5\, kg$ 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 ........... $N$.

$A$ bird weighs $2 \ kg$ and is inside a closed cage of $1 \ kg$. If it starts flying,then what is the weight of the bird and cage assembly in $kg$?

$A$ block placed on a rough inclined plane of inclination $\theta = 30^{\circ}$ can just be pushed upwards by applying a force $F$ as shown. If the angle of inclination of the inclined plane is increased to $\theta = 60^{\circ}$,the same block can just be prevented from sliding down by application of a force of the same magnitude $F$. The coefficient of friction between the block and the inclined plane is: