A uniform sphere of weight $w$ and radius $3\mathrm{ }\mathrm{m}$ is being held by a string of length $2\mathrm{ }\mathrm{m}$, attached to a frictionless wall, as shown in the figure. The tension in the string will be:

The acceleration of the block $B$ in the figure, assuming the surfaces and the pulleys $P_1$ and $P_2$ are all smooth and pulleys and string are light is $\frac{3F}{xm}$ then value of $x$ is.

In the arrangement shown in figure, the mass of the body $A$ is $n=4$ times that of body $B$. The height $h=20 \mathrm{cm}$. At a certain instant, the body $B$ is released and the system is set in motion. What is the maximum height (in $\mathrm{cm}$) the body $B$ will go up? Assume enough space above $B$ and $A$ sticks to ground. ($A$ and $B$ are of small size) $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

As shown to the right, two blocks with masses $m$ and $M(M>m)$ are pushed by a force $F$ in both Case $\mathrm{I}$ and Case $\mathrm{II}$. The surface on which blocks lie, is horizontal and frictionless. Let $R_I$ be the force that $m$ exerts on $M$ in case $\mathrm{I}$ and $R_{II}$ be the force that $m$ exerts on $M$ in

case $\mathrm{II}$. Which of the following statement is true?

The block $Q$ is pulled on a straight horizontal surface making an angle $\mathrm{\theta }$ with the horizontal. If $a$ is the acceleration of the block, $N$ the contact force by the surface, $T$ the pull of the string along with it and $M$ the mass of the block, then