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)

The pull $P$ is just sufficient to keep the $14 \mathrm{N}$ block in equilibrium as shown. Pulleys are ideal. Find the tension (in $N$) in the upper cable connected with ceiling.

In the arrangement shown in figure $m_1=1 \mathrm{kg}, m_2=2 \mathrm{kg}$. Pulleys are massless and string are light. For what value of $M$ the mass $m_1$ moves with constant velocity (Neglect friction)

In the figure shown $m_1=1 \mathrm{kg}, m_2=2 \mathrm{kg},$ pulley is ideal. At $t=0,$ both masses touches the ground and string is taut. A force $F=2 t$ is applied to pulley ($t$ is in second) then $m_1$ is lifted off the ground at time $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $m$ on a smooth horizontal surface is connected to a second mass $m$ by a light cord over a light frictionless pulley as shown. (Neglect the mass of the cord and of the pulley). A force of magnitude $F_{\circ }$ is applied to mass $m$ as shown. Neglect any friction. Find the value of force $F_{\circ }$ for which the system will be in equilibrium.