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The potential field of an electric field $\overrightarrow{E}=(y\hat{i}+x\hat{j})$ is

Two charges $+5\mu \text{C}$ and $+10\mu \text{C}$ are placed $20\text{cm}$ apart. The electric field at the mid-point between the two charges will be:

Find out the value of resistance $R$ in figure.

A stone projected with a velocity u at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity u at an angle $(\frac{\pi }{2}-\theta )$ with the horizontal, it reaches maximum height $H_2$.

The relation between the horizontal range R of the projectile, $H_1$ and $H_2$ is

An ideal gas with adiabatic exponent $\gamma$ is heated at a constant pressure. It absorbs total $Q$ amount of heat. Fraction of the heat used to increase its temperature of the gas is

A uniform constant magnetic field $\overrightarrow{B}$ is directed at an angle of ${45}^{\circ }$ to the $\text{x-axis}$ in the $\text{x-y}$ plane. $\text{PQRS}$ is a rigid, square wire frame carrying a steady current $I_o\left(\text{anticlockwise}\right)$, with its centre at origin $O$. At time $t=0$, the frame is at rest in the position shown in the figure with its sides parallel to the $x$ and $y$ axes. Each side of the frame is of mass $M$ and length $L$. What is the magnitude of torque $\tau$ about $O$ acting on the frame due to magnetic field?

What is optical path?

A ball rolls off the top of a stairway horizontally with a velocity of $4.5{\text{ms}}^{-1}$. Each step is $0.2\text{m}$ high and $0.3\text{m}$ wide. If $g$ is $10{\text{ms}}^{-2}$, then the ball will strike the edge of $n^{th}$ step, where $n$ is equal to

A ball is projected from ground with a velocity $v$ at an angle $\theta$ to the vertical. On its path, it makes an elastic collision with a vertical wall and returns to ground. The total time of flight of the ball is

Find the tension (in $N$) in the string connecting the $2m$ mass. (Strings are massless and inextensible)

Find out the effective length of a simple pendulum suspended at a place of $\text{g}=9.8{\text{m s}}^{-2}$, with a time period of $1\text{min}$.

A ball is thrown upward with an initial velocity $v_o$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^2$ (where, $m$ is mass of the ball, $v$ is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith (maximum height) is

If $F_1=10\text{N}$ and $F_2=20\text{N}$ as shown in the figure, the resultant $R$ will be [Hint: $\cos {65}^{\circ }=0.423$]

Interference fringes are produced by a double slit arrangement and a piece of plane parallel glass of refractive index $1.5$ is interposed in one of the interfering beam. If the fringes are displaced through $30$ fringe widths for light of wavelength $6\times {10}^{-5}\text{cm}$, find the thickness of the plate.

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Two short magnets of equal dipole moments $M$ are fastened perpendicularly at their centres, as given in the figure. The magnitude of the magnetic field at a distance $d$ from the centre of the bisector of the right angle is -



[Point $\text{P}$ lies on the equatorial axis of both magnets]

Locate the centre of mass of a uniform hemi spherical shell of radius R with reference to point 0 {as shown in figure}

Acceleration of $10\text{kg}$ block is given as $a=(20-2t){\text{m/s}}^2$, where $t$ is in $\text{seconds}$. Find the average impulse imparted to the block during the time interval $0$ to $5$ $\text{sec}$.

The stopping potential for the photoelectrons emitted from a metal surface of work function $1.7\text{eV}$ is $10.4\text{V}.$ Find the wavelength of the radiation used. Also identify the energy levels in hydrogen atom which will emit this wave length.

The gravitational force between two point masses $m_1$ and $m_2$ at separation r is given by $F=k\frac{m_1{m}_2}{r^2}$ The constant k

A flat disc of radius $R$ carries an excess charge on its surface. The surface charge density is $\sigma$. The disc rotated about an axis perpendicular to the plane passing through its center with angular velocity $\omega$. Find the torque on the disc , if it is placed in a uniform magnetic field $B$ directed perpendicular to the rotation axis:

Consider a rope of total mass $M$ and length $L$ suspended at rest from a fixed mount. The rope has a linear mass density that varies with height as $\lambda \left(z\right)={\lambda }_0\sin (\pi z\setminus L)$, where ${\lambda }_0$ is a constant. Constant gravitational acceleration $g$ acts downward.



The tension along the rope as a function of distance $z$ below the mount is