Determine tension $T_4$ in figure.

 

 A block of mass $25 \mathrm{kg}$ is raised by a $50 \mathrm{kg}$ man in two different ways as shown in figure. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of $700 \mathrm{N}$, which mode should the man adopt to lift the block without the floor yielding?

Consider the two configurations shown in equilibrium. I Find the ratio of $\frac{T_{\mathrm{A}}}{T_{\mathrm{B}}}$. (Ignore the mass of the rope and the pulley.)

A smooth box of mass $m$ is kept on an inclined plane of angle of inclination $\theta .$ A force $F$ is applied on the box.

If the box does not lose contact, find acceleration of the block.

A solid sphere of mass $2 \mathrm{kg}$ is resting inside a cube as shown in the figure. The cube is moving with a velocity $\overrightarrow{v}=\left(5t\hat{\mathrm{i}}+2t\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Here, $t$ is time in $\mathrm{seconds}$. All surfaces are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube?

Two blocks $m$ and $M$ are placed on a platform that moves up with an upward acceleration $a$. Find the normal reaction between the blocks and the normal reaction on the block exerted by the platform.

The masses of blocks $A$, $B$ and $C$ are $1 \mathrm{kg}$, $2 \mathrm{kg}$ and $0.5 \mathrm{kg}$, respectively. All surfaces are smooth. If the force $F=50 \mathrm{N}$ acts as shown in the figure at the instant shown, find the force which $A$ exerts on $B$ and the acceleration of $C$.

Seven identical dominoes (i.e., blocks) each of mass $m=1 \mathrm{kg}$ are to be stacked in three columns (figure gives an example) and pushed across a frictionless ice rink by a horizontal $10 \mathrm{N}$ force. Assume dominoes do not slip with respect to each other. How many dominoes should be in each column, with a minimum of one,

$\left(\mathrm{a}\right)$ to maximise the acceleration of the dominoes?

$\left(\mathrm{b}\right)$ to maximise the force on the column $C$ due to column $B$

An inclined plane is moved towards the right with an acceleration of $5 \mathrm{m} {\mathrm{s}}^{-2}$ as shown in the figure. Find the force in newton which block of mass $5 \mathrm{kg}$ exerts on the inclined plane. (All surfaces are smooth.)