Laws of Motion

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^{\circ}$, the box starts to slip and slides $4.0m$ down the plank in $4.0s$. The…

Two blocks $A$ and $B$ of masses $3m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of…

A block of mass m is placed on a smooth inclined wedge $ABC$of inclination $\theta\,$as shown in the figure. The wedge is given an acceleration $a$towards the right. The relation between $a$ and $\theta\,$ for the block…

A block $\text{A}$ of mass $m_{1}$ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block $\text{B}$ of mass $m_{2}$ is…

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 $0.05.$($g=10ms^{-2},$ mass of the string is negligible and no…

A stone of mass $900g$ is tied to a string and moved in a vertical circle of radius $1m$making $10\mathrm{rpm}$. The tension in the string, when the stone is at the lowest point is (if $\pi\,^{2}=9.8$and $g=9.8ms^{-2}$)

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 $0.2ms^{-2}.$ The normal reaction $R^{'}$…

As shown in the figure a block of mass $10\mathrm{kg}$ lying on a horizontal surface is pulled by a force F acting at an angle $30^{\circ}$, with horizontal. For $\mu\,_{s}=0.25$, the block will just start to move for…

The figure represents the momentum time $(p-t)$ curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum…

A mass of $10\mathrm{kg}$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45^{\circ}$ at the roof point. If the suspended…

A block takes $t$ time to slide down a plane inclined at $45^{\circ}$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\dfrac{t}{2}$ to slide down the plane. The coefficient of…

A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ}$ with an acceleration of $\frac{\mathrm{g}}{2}$, the value of coefficient of kinetic friction is