$A$ boy of mass $4 \, kg$ is standing on a piece of wood having mass $5 \, kg$. If the coefficient of friction between the wood and the floor is $0.5$,the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ...... $N$. (Round off to the Nearest Integer) [Take $g = 10 \, m s^{-2}$]

An infinite number of masses are placed on a frictionless table and they are connected via massless strings. Their masses follow the sequence $m, \frac{m}{2}, \frac{m}{6}, \ldots, \frac{m}{n!}, \ldots$ and they are further connected to a mass $m$ that hangs over a massless pulley. The acceleration of the hanging mass is

$A$ body of mass $6 \,kg$ is moving with a uniform velocity $4 \,m/s$. Its velocity changes to $6 \,m/s$ when a force of $12 \,N$ acts on it. Then its displacement is (in $\,m$)

Consider two blocks of mass $m_1 = 5 \, kg$ and $m_2 = 10 \, kg$ placed on a horizontal surface. The coefficient of static friction between the blocks and the surface is $\mu = 0.2$. $A$ horizontal force $F$ is applied to the $10 \, kg$ block. What is the maximum force $F$ (in $N$) that can be applied such that neither block moves? (Take $g = 10 \, m/s^2$)

$A$ man is standing on a spring platform. The reading of the spring balance is $60\, kg$ wt. If the man jumps off the platform,what happens to the reading of the spring balance?

$A$ force of $36 \, \text{dyne}$ acts on a body placed on an inclined plane making an angle of $60^{\circ}$ with the horizontal. If the mass of the body is $18 \, \text{g}$,what is the acceleration of the body in the horizontal direction?