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A rope of mass $2m$ is used to pull a block of mass $m$ as shown in the figure. Find the force exerted by the rope on the block. Assume all surfaces as frictionless.

A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is seconds. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is

When a mass of $8\text{kg}$ is suspended from a string, its length is $l_1$. If a mass $10\text{kg}$ is suspended, its length is $l_2$. Length, when a mass of $16\text{kg}$ is suspended from it, is given by

A circular loop carrying a current i has wire of total length L. A uniform magnetic field B exists parallel to the plane of the loop. (a) Find the torque on the loop. (b) If the same length of the wire is used to form a square loop, what would be the torque ? Which is larger ?

Three current carrying elements having same length carries current $i,2i$ and $4i$ respectively. Magnetic fields due to wires be $B_1,B_2$ and $B_3$ respectively at a point $\text{P}$ whose distance from the current elements is $r,2r$ and $4r$ respectively. Then, $B_1:B_2:B_3$ is

Two particles, having masses in the ratio $n:1$, are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released from rest, the acceleration of the centre of mass of the system is,

If the radius of the earth contracts to half of its present value without a change in its mass, then new duration of the day will be;

A solid sphere of mass $m$ and radius $R$ is released from the top of an inclined plane of inclination $\theta$. The minimum coefficient of friction between the plane and the sphere so that it rolls down the plane without sliding is given by

A potential difference created between the two plates in the photoelectric experiment setup helps to accelerate the photoelectrons, so that all of them reach the collector plate and contribute to the current. In the absence of such an accelerating potential, will there be any photocurrent at all? (Assume the photoelectrons come out perpendicular to the emitter plate.)

A block moving horizontally on a smooth surface with a speed of $20{\text{ms}}^{-1}$ bursts into two equal pieces continuing in the same direction. If one of the points moves at $30{\text{ms}}^{-1}.$ Find the fractional change in kinetic energy.

Let the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ be perpendicular to each other. Then a vector $\overrightarrow{v}$ in terms of $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying the equation $\overrightarrow{v}\cdot \overrightarrow{a}=0,$ $\overrightarrow{v}\cdot \overrightarrow{b}=1$ and $\left[\overrightarrow{v}\overrightarrow{a}\overrightarrow{b}\right]=1$ is

Two large conducting plates are placed parallel to each other with a separation d. An electron (-e, m) starting from rest near one of the plates reaches the other plate in time $t_0$. Find the surface charge density on the inner surface.

A large tank is filled with water to a height $H$. A small hole is made at the base of the tank. It takes $T_1$ time to decrease the height of water to $\frac{H}{\eta }(\eta >1),$ and it takes $T_2$ time to take out the rest of the water. If $T_1=T_2,$ then the value of $\eta$ is

A rod is of length 2 m and of mass 1 kg. Moment of inertia about an axis perpendicular to its length and passing through one of its end is

In sports, the timing of a 200 m straight dash is recorded at the finish point on hearing the sound of a gun fired at the starting point. The time recorded will be more accurate

For a common base configuration of PNP transistor, the gain$\left(\alpha \right)$ is 0.98, then current gain of common emitter configuration will be

Find the period of small oscillation of the bob of mass m as shown in the figure. Mass of the rod is m.

1. 10

A particle is projected up the incline such that its component of velocity along the incline is $10\text{m/s}$. Time of flight is $2\text{sec}$ and maximum height above the incline is $5\text{m}$. Then velocity of projection will be

A body of mass '$m$' and radius '$r$' is released from rest along a smooth inclined plane of angle of inclination $\theta$. The angular momentum of the body about the instantaneous point of contact after a time '$t$' from the instant of release is equal to? (assume the inclined to be of indefinite length)

The closest distance of approach of an $\alpha$ - particle travelling with a velocity $v$ towards a stationary nucleus is $d$. For the closest distance to become $\frac{d}{2}$ towards a stationary nucleus of double the charge, the velocity of projection of the $\alpha$- particle has to be

If velocity of a particle is $v\left(t\right)=6t^2\text{m/s}$, the average speed of the particle in $6\text{sec}$ is

The resonant frequency of a circuit is f. If the capacitance is made 16 times the initial values, then the resonant frequency will become

A $YDSE$ apparatus is as shown in figure below. The condition for point $P$ to be a dark fringe is $(\lambda =$ wavelength of the light used)

when two bodies approach each other with different speeds the distance between them decreases by 120m for every one minute if they are moving in the same direction the distance between them increases by 90 m for everyone minutes the speeds of the bodies are

An electric dipole with dipole moment $\frac{P_0}{\sqrt{2}}(\hat{i}+\hat{j})$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $E_0$. If the potential is constant on a circle of radius R centered at the origin as shown in the figure, then the correct statement (s) is/are : (${\in }_0$ is permittivity of free space. R >> dipole size)