Laws of Motion

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 $R^{'}$…

An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field $200\frac{N}{C}$ as shown in the figure. A body of mass $1\mathrm{kg}$and charge $5\mathrm{mC}$ is…

The normal reaction $N$for a vehicle of $800\mathrm{kg}$ mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is ____$\times\,10^{3}\mathrm{kg}ms^{-2}$?

A uniform metal chain of mass $m$and length $L$passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$is hanging on one side and rest of its length $L-l$is hanging on the…

The motion of a mass on a spring, with spring constant $K$ is as shown in figure. The equation of motion is given by,$x(t)=A\sin\,\omega\,t+$$B\cos\,\omega\,t$with$\omega\,=\sqrt{\frac{K}{m}}$. Suppose that at time…

Three blocks $A,B$and $C$ are pulled on a horizontal smooth surface by a force of $80N$ as shown in figure. The tensions$T_{1}\text{and}T_{2}$in the string are respectively:

Consider a block kept on an inclined plane (inclined at $45^{\circ}$) as shown in the figure. If the force required to just push it up the incline is $2$ times the force required to just prevent it from sliding down,…

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point…

A block of mass $5\mathrm{kg}$ is placed on a rough inclined surface as shown in the figure. If$\vec{F}_{1}$is the force required to just move the block up the inclined plane and$\vec{F}_{2}$is the force required to…

A disc with a flat small bottom beaker placed on it at a distance $R$from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega\,$. The…

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$. the acceleration of the system is…

A block of mass $M$ slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $\theta\,$. The magnitude of the contact force will be :