A $T$ shaped object with dimensions as shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $AB$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$.

In the pulley system shown, if the radii of the bigger and smaller pulleys are $2 \mathrm{m}$ and $1 \mathrm{m}$, respectively, and the acceleration of block $\mathrm{A}$ is $5 \mathrm{m} {\mathrm{s}}^{-2}$ in the downward direction, then the acceleration of block $\mathrm{B}$ will be:

A uniform rod of mass $15\mathrm{}\mathrm{k}\mathrm{g}$ is held stationary with the help of a light string as shown in figure. The tension in the string is

Four forces of the same magnitude act on a square as shown in figure. The square can rotate about point $O$; mid point of one of the edges. The force which can produce greatest torque is

Uniform rod $AB$ is hinged at end $A$ in horizontal position as shown in the figure. The other end is connected to a block through a massless string as shown. The pulley is smooth and massless. Masses of block and rod is same and is equal to $m$. Then acceleration of block just after release from this position is

A cubical block of side $L$ rests on a rough horizontal surface with coefficient of friction $\mu .$ A horizontal force $F$ is applied on the block as shown If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is