The $50 \mathrm{kg}$ homogeneous smooth sphere rests on the $30°$ incline $A$ and bears against the smooth vertical wall $B.$ The contact forces at $A$ and $B.$

A mass $\mathrm{M}$ is suspended by a rope from a rigid support at $A$ as shown in figure. Another rope is tied at the end $B,$ and it is pulled horizontally with a force $F.$If the rope $AB$ makes an angle $\theta$ with the vertical in equilibrium, then the tension in the string $AB$ is :

Two blocks of $7 \mathrm{kg}$ and $5 \mathrm{kg}$ are connected by a heavy rope of mass $4 \mathrm{kg}.$ An upward force of $200 \mathrm{N}$ is applied as shown in the diagram. The tension at the top of heavy rope at point $P$ is $\left(g=10 {\mathrm{ms}}^{-2}\right)$

Two masses are connected by a string which passes over a pulley accelerating upward at a rate $A$ as shown. If $a_1$ and $a_2$ be the acceleration of bodies $1$ and $2$, respectively then