A small object is suspended at rest from two strings as shown in figure. The magnitude of the force exerted by each string on the object is $10\sqrt{2} \mathrm{N}$. Find the magnitude of the mass of the object.

  

The object in figure weighs $40 \mathrm{kg}$ and hangs at rest. Find the tensions in the three cords that hold it.

A block of mass $m=10 \mathrm{kg}$ is suspended with the help of three strings as shown in figure. Find the tensions $T_1$and $T_2$.
 

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.