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…

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…

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 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…

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$60HP$electric motor lifts an elevator having a maximum total load capacity of$2000kg.$If the frictional force on the elevator is$4000N,$the speed of the elevator at full load is close to :$(1HP=746W,g=10ms^{-2})$

What will be the acceleration due to gravity at a depth $d$, where $g$ is acceleration due to gravity on the surface of earth?

A point mass m is moved in a vertical circle of the radius r with the help of a string. The velocity of the mass is 7gr at the lowest point. The tension in the string at the lowest point is:

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity g…

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular…

A car is negotiating a curved road of radius \$\text{R}$. The road is banked at an angle \$\theta$. The coefficient of friction between the tyres of the car and the road is \$\mu_{s}$. The maximum safe velocity on this…

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8$\times$10-4 J by…