Laws of Motion

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 block of $\sqrt{3}\mathrm{kg}$is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension $T$ is :…

A string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $\left(\frac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown.…

A tube of length $50\mathrm{cm}$ is filled completely with an incompressible liquid of mass $250g$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular…

As shown in the figure, a block of mass $\sqrt{3}\mathrm{kg}$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$. The critical force to be applied on the vertical surface as shown at…

A car is moving on a plane inclined at $30^{\circ}$ to the horizontal with an acceleration of $10ms^{-2}$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which…

A body of mass $1\mathrm{kg}$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $FN$. The…

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 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 $g=9.8ms^{-2}$)

The coefficient of static friction between a wooden block of mass $0.5\mathrm{kg}$ and a vertical rough wall is $0.2.$ The magnitude of the horizontal force that should be applied on the block to keep it adhere to 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…

As shown in figure, a $70\mathrm{kg}$garden roller is pushed with a force of $\vec{F}=200N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g=10ms^{-2}$)