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A solid sphere of radius $R$ has total charge $Q$, uniformly distributed. Find the minimum work done to decrease the radius of the sphere to $\frac{R}{2}$.

If $\overrightarrow{E}$ = 2i +3j +4k and $\overrightarrow{A}$ = 3i +2j +4k. What is the flux of the given $\overrightarrow{E}$ through the area?

Given, $m_A=30\text{kg},m_B=10\text{kg}$ and $m_C=20\text{kg}$. The co-efficient of friction between $\text{A}$ and $\text{B}$ is ${\mu }_1=0.3$, between $\text{B}$ and $\text{C}$ is ${\mu }_2=0.2$ and between $\text{C}$ and ground is ${\mu }_3=0.1$. The least horizontal force $F$ required to start motion of any part of the system of three blocks resting upon the another as shown below is-

The equation of a standing wave, produced on a string fixed at both ends, is $y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

What could be the smallest length of the string?

If $\underset{0}{\overset{\alpha }{\int }}\frac{dx}{1-\cos \alpha \cos x}=\frac{A}{\sin \alpha }+B(\alpha \ne 0),$ then possible values of $A$ and $B$ are

A horizontal rod of length $l=2\text{m}$ and mass $2\text{kg}$ with the balls $\text{A}$ and $\text{B}$ of mass $1\text{kg}$ each at its ends is clamped at the centre $\text{C}$ in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle $P$ of mass $1\text{kg}$ is dropped from a height of $5\text{m}$ on the ball $B$. The particle collides with $B$ and sticks to it. Find the angular velocity of the system just after the collision.

The resistance of wire at ${20}^{\circ }C$ is $20\Omega$, and at ${300}^{\circ }C$ resistance of wire is $50\Omega$. The temperature at which its resistance will be $40\Omega$ is

Neglecting friction and the effect of small bend near bottom, the time period of oscillations of the particle shown in the figure is $g=10m/s^2$

A ray is passing through a broken prism as shown. Find the total deviation suffered by the light ray.

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The root mean square speed of a gas molecule is $300\text{m/s}$. What will be the root mean square speed of the molecules if the atomic mass is doubled and absolute temperature is halved?

The maximum speed of a particle executing S.H.M. is 1m/s and its maximum acceleration is 1.57m/$se{c}^2$ . The time period of the particle will be

[DPMT 2002]

The magnitude of the gravitational force at distance $r_1$ and $r_2$ from the centre of a uniform sphere of radius R and mass M are $F_1$ and $F_2$ respectively. Then,

A block of mass $2\text{kg}$ is put on a rough horizontal surface having coefficient of friction $0.5$. The acceleration of block and frictional force acting on block if $F=5\text{N}$ is (Take $g=10{\text{m/s}}^2$)

A small sphere of radius $R$, is held against the inner surface of a smooth spherical shell of radius $6R$ as shown in the figure. The masses of the shell and small sphere are $4M$ and $M$ respectively. This arrangement is placed on a smooth horizontal table. The small sphere is now released. The x-coordinate of the centre of the shell when the smaller sphere reach the other extreme position is,

Find the force $F$ acting on the body of mass $6\text{kg}$ to move it with an acceleration of $1.5{\text{m/s}}^2$. Take $g=10{\text{m/s}}^2$.

A wave disturbance in a medium is described by y(x , t)= 0.02 cos (50 $\pi$ t + $\frac{\pi }{2}$) cos (10 $\pi$x) where x and y are in metre and t in second

A fish rising vertically up towards the surface of water with speed $3{\text{ms}}^{-1}$ observes a bird diving vertically down towards it with speed $9{\text{ms}}^{-1}$. The actual velocity of the bird is

What is the work done in moving a unit positive charge when the potential difference applied across the ends of the conductor is $10V$?

If a prism of dispersive power $0.021$ and refractive index $1.53$ forms an achromatic combination with a prism having the prism of angle ${4.2}^{\circ }$, dispersive power $0.045$ and refractive index $1.65,$ then what is the resultant deviation of the combination?

Why electric potential difference is scalar quantity even there is the direction of electrons.

Vector $\overrightarrow{A}$ is 2 cm long and is ${60}^{\circ }$ above the +ve X axis. Vector $\overrightarrow{A}$ is 2 cm long and is ${60}^{\circ }$ below the x - axis in the fourth quadrant. The value of $\overrightarrow{A}$ + $\overrightarrow{B}$ is

An equilateral triangular loop having a resistance $R$ and length of each side $l$ is placed in a magnetic field which is varying at $\frac{dB}{dt}=1\text{T/s}$. The induced current in the loop will be