A block of mass  $m$ is placed on a frictionless inclined plane of angle $\theta$. What  is the acceleration of the block when it is released? Calculate the time taken by the block to reach the bottom and its speed at the bottom.

 

 

A steel block of $10 \mathrm{kg}$ rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2 \mathrm{m} {\mathrm{s}}^{-2}.$ The normal reaction $R^{\text{'}}$ by the floor if mass of the iron cylinders are equal and of $20 \mathrm{kg}$ each is $\left(\text{in} \mathrm{N}\right)$,

[Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $\left.{\mu }_{\mathrm{s}}=0.2\right]$

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 boy of mass $4 \mathrm{kg}$ is standing on a piece of wood having mass $5 \mathrm{kg}$. If the coefficient of friction between the wood and the floor is $0.5 ,$ the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is _______ $\mathrm{N}$. (Round off to the Nearest Integer)

[Take $\left.g=10{ \mathrm{m} \mathrm{s}}^{-2}\right]$

An object of mass $m$ is being moved with a constant velocity under the action of an applied force of $2 \mathrm{N}$ along a frictionless surface with following surface profile.

The correct applied force vs distance graph will be :

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is $0.05.$ ($g=10 \mathrm{m} {\mathrm{s}}^{-2},$ mass of the string is negligible and no other friction exists).

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is:
Given $m=8 \mathrm{kg}, M=16 \mathrm{kg}$
Assume all the surfaces shown in the figure to be frictionless.

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 bodies $A$ and $B$ of masses $5 \mathrm{kg}$ and $8 \mathrm{kg}$ are suspended from a rigid support by inextensible massless strings as shown in figure. If the whole system is accelerated upwards at $2{ \mathrm{ms}}^{-2}$, the tension in each string is $\left(\mathrm{g}=10{ \mathrm{ms}}^{-2}\right)$

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

A block of mass $40 \mathrm{kg}$ slides over a surface, when a mass of $4 \mathrm{kg}$ is suspended through an inextensible massless string passing over frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is $0.02$. The acceleration of block is: (Given $g=10{ \mathrm{m} \mathrm{s}}^{-2}$.)

In the arrangement shown in figure $a_1,a_2,a_3$ and$a{ }_{4 }$  are the accelerations of masses $m_1,m_2,m_3$ and $m_4$ respectively. Which of the following relation is true for this arrangement?

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)

The machine as shown has $2$ rods of length $1 \mathrm{m}$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a $2 \mathrm{kg}$ weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :