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Two bodies of masses $3\text{kg}$ and $2\text{kg}$ are located at $x=0\text{m}$ and $x=4\text{m}$ respectively. Find the position of the centre of mass of the system (with respect to mass $2\text{kg}$) .

The sphere shown in figure lies on a rough plane when a particle of mass m travelling at a speed v0 collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find the linear speed of the combined system just after the collision. Assume that the mass M of the sphere is large compared to the mass of the particle so that the centre of mass of the combined system is not appreciably shifted from the centre of the sphere.

1. 6.512

1. 10392.304

A particle of charge $q$ and mass $m$ starts moving from the origin under the action of electric field $\overrightarrow{E}=E_0\hat{i}$ and $\overrightarrow{B}=B_0\hat{i}$ with velocity $\overrightarrow{V}=V_0\hat{j}$. The speed of particle will become $2V_0$ after a time:

A boy's catapult is made of rubber cord which is $42cm$ long, with $6mm$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02kg$ on it and stretches the cord by $20cm$ by applying a constant force. When released, the stone flies off with a velocity of $20m{s}^{-1}$. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to

A force $F=\frac{-k}{x^2}(x\ne 0,(k\left)\text{is a positive constant}\right),$ acts on a particle in $x$ direction. The work done by this force in displacing the particle from $x=+a$ to $x=+2a$ is

If the angular momentum of a planet of mass $m$, moving around the Sun in a circular orbit is $L$, about the centre of the Sun, its areal velocity is:

Sodium metal crystallizes in B.C.C lattice with edge length of $4.29\dot{A}$. The radius of sodium atom is

The electric field intensity due to a thin infinitely long wire of uniform linear charge density $\lambda$ at $\text{O}$ as shown in the figure is

What is the value of linear velocity, if $\overrightarrow{\omega }=3\hat{i}-4\hat{j}+\hat{k}$ and $\overrightarrow{r}=5\hat{i}-6\hat{j}+6\hat{k}$

A point charge $q$ is placed near to an infinitely large plane. Find flux through the plane.

A particle executes linear $\text{SHM}$ with a time period of $10\text{s}$. Find the time taken by the particle to go directly from its mean position (at $t=0)$ to $\frac{1}{2}$ of its amplitude.

Let
us list some of the factors, which could possibly influence the speed
of wave propagation:

(i)
Nature of the source.

(ii)
Direction of propagation.

(iii)
Motion of the source
and/or observer.

(iv)
Wave length.

(v)
Intensity of the wave.

On
which of these factors, if any, does

(a)
The speed of light in
vacuum,

(b)
The speed of light in a
medium (say, glass or water), depend?

A boy travels from $A$ to $B$ at a speed of $2.5\text{km/hr}$ and returns at a speed of $0.5\text{km/hr}$. The average speed of the boy for the whole journey is

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$, the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ at constant pressure $P$, is :-

A car of mass ‘m’ is driven with acceleration ‘a’ along a straight level road against a constant external resistive force ‘R’. When the velocity of the car is ‘v’, the rate at which the engine of the car is doing work will be

A single acting $N{H}_3$ compressor follows the compression law $(P{V}^{1.1}=C)$. The operating pressure for the vapour compression refrigeration are: 2.3637 bar $(-{15}^{\circ }C$) and 11.671 bar $(+{30}^{\circ }C$). The enthalpy at the exit of compression is 1560 kJ/kg. If refrigerant enters dry saturated to the compressor, then what is the heat loss from the compressor? The refrigeration capacity of the refrigerator is 10 tons..

A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray incident from left, that is parallel to the principal axis, exits parallel to the incident ray as shown. The refractive index n of the material of the cylinder is

A body of mass $2\text{kg}$ is kept on a rough horizontal surface. If ${\mu }_s=0.5$ and an external force of $F=5\text{N}$ is applied on the body, find the angle of friction.

(Take $g=10{\text{m/s}}^2$)

The ratio of the longest to the shortest wavelengths in Balmer series of hydrogen spectra is-

A $2\text{kg}$ block slides on a horizontal floor with a speed of $4\text{m/s}$. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic friction force is $15\text{N}$ and spring constant is $10,000\text{N/m}$. The spring compresses by

Two sound waves (expressed in CGS units) given by $y_1=0.3sin\frac{2\pi }{\lambda }(vt-x)$ and $y_2=0.4sin(vt-x+\theta )$ and interfere. The resultant amplitude at a place where phase difference is $\frac{\pi }{2}$ will be

[MP PET 1991]

Why the net current is conduction current plus drift current? Basically in the previous chapter we learnt about impedence is R+iX.As such why should it be not = ic+ I.d or square root of Ic square plus I'd square, just like impedence?