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 $.3$)

$A$ system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction $= \mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (Assume $m_1 = m_2 = m_3 = m$)

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

$A$ motor car moving with velocity $7 \ m/s$ stops in $10 \ m$ distance when brakes are applied. What is the relation between the resistance force $(R)$ and the weight $(W)$ of the car? (Take value of $g = 9.8 \ m/s^2$)

$A$ 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:

Three forces of magnitude $F_1, F_2$ and $F_3$ act on a body located at the origin as shown in the figure. The condition that gives zero net force is