A block is dragged on a smooth plane with the help of a rope which moves with a velocity $v$ as shown in figure. The horizontal velocity of the block is

In the figure, mass of a ball is $\frac{9}{5}$ times mass of the rod. Length of rod is $1 \,m$. The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod. (in $S$)

For the given diagram when block $B$ is pulled with velocity $V$ then velocity of block $A$ will be :-

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8\; {kg}$ to strike the ground starting from rest. (use $\left.{g}=10\, {m} / {s}^{2}\right)$ (in ${s}$)

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass $2 \mathrm{~kg}$ is :

Two masses $M _{1}$ and $M _{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M _{2}$ is twice that of $M_{1}$. the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$. The acceleration of The system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be.