A block of mass $M$ is pulled along a smooth horizontal surface with a rope of mass $m$ by applying a force $F.$ The acceleration of the block will be

Calculate the tensions $T_1, T_2$ and $T_3$ in the three threads shown in the following figure. (All threads are massless) $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A heavy block of mass $M$ hangs in equilibrium at the end of a rope of mass $m$ and length $l$ connected to a ceiling. Determine the tension in the rope at a distance $x$ from the ceiling.

The magnitude of difference in accelerations of blocks of mass $m$ in both the cases shown below is

Find the tension $T$ needed to hold the cart in equilibrium, if there is no friction.

Two blocks of masses $M_1$ and $M_2$ are connected to each other through a light spring as shown in figure. If we push mass $M_1$ with force $F$ and cause acceleration $a_1$ in mass $M_1$, what will be the magnitude of acceleration in $M_2$?

A mass $2 \mathrm{m}$ lies on a fixed, smooth cylinder. An ideal string attached to $2 \mathrm{m}$ passes over the cylinder to mass $m.$ Then the value of angle $\theta$ for which system is in equilibrium

Figure shows a block of mass $2 \mathrm{m}$ sliding on a block of mass $m.$ Find the acceleration of each block. (All surface are smooth)