A small ball of mass $M$ is held in equilibrium with two identical springs as shown in the figure. Force constant of each spring is $k$ and relaxed length of each spring is $\frac{\mathcal{l}}{2}$. What is distance between the ball and roof?

The ideal mechanical advantage (i.e. the ratio of the weight $W$ to the pull $P$ for equilibrium) of the combination of pulleys shown is:

A block resting on a smooth inclined plane is acted upon by a force $F$ as shown. If mass of block is $2 \mathrm{kg}$ and $F=20 \mathrm{N}$ and $\sin 37°=\frac{3}{5}$, the acceleration of block is

A block of mass $3 \mathrm{kg}$ is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be $\left(g=10\mathit{ }\mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $\mathrm{m}=2 \mathrm{kg}$ is resting on a rough inclined plane of inclination $30°$ as shown in shown in figure. The coefficient of friction between the block and the plane is $\mu =0.5$. What minimum force $F$ should be applied perpendicular to the plane on the block, so that block does not slip on the plane $\left(g=10 \mathrm{m} {\mathrm{s}}^{-1}\right)$

A $40 \mathrm{kg}$ slab rests on a frictionless floor. A $10 \mathrm{kg}$ block rests on top of the slab. The static coefficient of friction between the block and slab is $0.60$ while the kinetic coefficient is $0.40$. The $10 \mathrm{kg}$ block is acted upon by a horizontal force of $100 \mathrm{N}$. If $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$, the resulting acceleration of the slab will be-

In the arrangement shown in the figure, mass of the block $B$ and $A$ is $2 \mathrm{m}$ and $m$ respectively. Surface between $B$ and floor is smooth. The block $B$ is connected to the block $C$ by mass means of a string pulley system. If the whole system is released, then find the minimum value of mass of block $C$ so that $A$ remains stationary w.r.t. $B$. Coefficient of friction between $A$ and $B$ is $\mu$.