Slides in the park is polished smooth so that

An inclined plane making an angle of $30°$ with the horizontal is placed in a uniform horizontal electric field $200\frac{\mathrm{N}}{\mathrm{C}}$ as shown in the figure. A body of mass $1 \mathrm{kg}$ and charge $5 \mathrm{mC}$ is allowed to slide down from rest at a height of $1 \mathrm{m}$. If the coefficient of friction is $0.2,$ find the time taken by the body to reach the bottom.
$\left[g=9.8 \mathrm{m} {\mathrm{s}}^{-2}; \sin 30°=\frac{1}{2}; \cos 30°=\frac{\sqrt{3}}{2}\right]$

Two blocks $A$ and $B$ of masses $1.5 \mathrm{kg}$ and $0.5 \mathrm{kg}$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block A is lifted until block B touches the ground and then block A is released. The initial height of block A is $80 \mathrm{cm}$ when block B just touches the ground. The maximum height reached by block $\mathrm{B}$ from the ground after the block A falls on the ground is

A student skates up a ramp that makes an angle $30°$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path $xyz$ of radius $R$ during which he/she reaches a maximum height $h$ (at point $y$) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then ($g$ is the acceleration due to gravity)

On a smooth table two blocks are placed two blocks in contact. A horizontal force of  $5 \mathrm{N}$ is applied on the $20 \mathrm{kg}$ block as shown. If this force is applied on the other side of $10 \mathrm{kg}$ block, The force with which  $20 \mathrm{kg}$ block will press the $10 \mathrm{kg}$ block is _____ $\mathrm{N}$ (up to two decimal places)

At $t=0,$ force $F=kt$ is applied to a small body of mass $m$ resting on a smooth horizontal plane $(k$ is a constant $)$. The force is at an angle $\mathrm{\theta }$ with the horizontal.

Then the velocity of the body when its breaking off the plane is

System shown in Fig. $7.64$ is in equilibrium and at rest. The spring and the string are massless, now the string is cut. The acceleration of mass $2 \mathrm{m}$ and $\mathrm{m}$ just after the string is cut will be