Nature of Physical Laws

A ball of mass 5kg moving at 3m/s collides with another ball of mass 3kg moving at 5m/s in the same direction. If the balls move together after the collision in the same direction, find their common velocity.

Rockets work on the principle of conservation of _____

The law of conservation of energy is applicable to mechanical systems as they require energy input to keep working

In a particle accelerator, a current of $500 \mu A$ is carried by a proton beam in which each proton has a speed of $3\times {10}^7 m/s$. The cross-sectional area of the beam is $1.50 m{m}^2.$ The charge density in this beam (in $\left.C/m^3\right)$ is close to
 

Bernoulli’s theorem is nothing but a statement of conservation of _____ for liquids.

Charge can neither be created nor destroyed.

A bomb at rest explodes into three parts of the same mass. The linear momentum of two parts are $-2P \widehat{i}$ and $P\widehat{j}$ . The magnitude of momentum of third part is $P\sqrt{x}$ . Find $x$ .

A planet revolves around a massive star in the elliptical orbit shown. Point A on the orbit corresponds to perigee. Consider motion of the planet from position P to position Q. About A, angular momentum of the planet

The figure here shows a uniform rod of mass m and length $l$ at rest, in a gravity free region. The rod is hinged at one of its ends. The rod is oriented along $y‐$axis, in the position shown here.



Suppose that a particle of mass m moving parallel to $x‐$axis strikes the rod and comes to rest. Distance from the hinge where the particle strikes the rod, so that linear momentum of the 'particle plus rod' system is conserved, is

The figure here shows a uniform rod of mass m and length $\mathcal{l}$ at rest, in a gravity free region. The rod is hinged at one of its ends. The rod is oriented along y - axis, in the position shown here.

Suppose that a particle of mass m moving parallel to x - axis strikes the rod elastically and comes to rest. Distance from the hinge where the particle strikes the rod equals

A positively charged rod is brought near an uncharged conductor. If the rod is then suddenly withdrawn, the charge left on the conductor will be

In an explosion, a body breaks up into two pieces of unequal masses. In this

A body of mass $1000\mathrm{ }\mathrm{k}\mathrm{g}$ is moving horizontally with a velocity $50 \mathrm{m} {\mathrm{s}}^{-1}$. A mass of $250\mathrm{ }\mathrm{k}\mathrm{g}$ is added. Find the final velocity.

The blocks of mass $m$ each are connected to a spring of spring constant $k$ as shown in figure. The maximum displacement in the block is

A dancer is standing on a stool rotating about the vertical axis passing through its centre. She pulls her arms towards the body reducing her moment of inertia by factor of n. The new angular speed of turn table is proportional to

A railroad hand car is moving along straight frictionless track. In each of the following cases the car initially has a total mass (car and contents) of $200 \mathrm{kg}$ and is travelling with a velocity $4 \mathrm{m} {\mathrm{s}}^{-1}$. Find the final velocity (in$\mathrm{m} {\mathrm{s}}^{-1}$) of the car if a $20 \mathrm{kg}$ mass is thrown sideways out of the car with a velocity $2 \mathrm{m} {\mathrm{s}}^{-1}$ relative to the car.