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Light of wavelength 5000 $\stackrel{\circ }{A}$ falls on a sensitive plate with photoelectric work function of 1.9 eV. The kinetic energy of the photoelectron emitted will be

In an electromagnetic wave, the amplitudes of magnetic field $\left(B_0\right)$ and electric field $\left(E_0\right)$ in free space are related as :

An optical fibre $(\mu =1.72)$ is surrounded by a glass coating $(\mu =1.50)$. Find the critical angle for total internal reflection at the fibre-glass interface.

The current as a function of time through a $4.6\text{H}$ inductor is shown in the following graph. The induced emf during the time interval $t=5\text{ms}$ to $6\text{ms}$ will be -

Find the normal force and acceleration respectively of the $2\text{kg}$ block shown in the figure.

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

The vector projection of a vector $3\hat{i}+4\hat{j}$ on y-axis is

An ideal massless spring $S$ can be compressed by $1m$ by a force of $100N$ in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane at ${30}^{\circ }$ to the horizontal. A $10kg$ block $M$ is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by $2m$. If $g=10m/s^2$, what is the speed of mass just before it touches the spring?

The parabola $y^2=2x$ divides the circle $x^2+y^2=8$ in two parts. Then, the ratio of the areas of these parts is:

An electron at rest has a charge of $1.6\times {10}^{-19}\text{C}$. It starts moving with a velocity $v=\frac{c}{2}$, where $c$ is the speed of light, then the new charge on it is

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.5 s for the boat to travel from its highest point to its lowest a total distance of 0.62m. The fisherman sees that the wave crests are spaced 6.0 m apart. What would be the equation of such a wave?

A wire has a resistance of $24\Omega$. If the length of the wire is tripled, then the resistance of the wire will become -

Two stars of masses $3\times {10}^{31}\text{kg}$ each, and at distance $2\times {10}^{11}\text{m}$ rotate in a plane about their common centre of mass $O$. A meteorite passes through $O$ moving perpendicular to the star 's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at $O$ is



Take Gravitational constant $G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{kg}}^{-2})$

The number of possible natural oscillations of air column in a pipe closed at one end of length $85\text{cm}$ whose frequencies lie below $1250\text{Hz}$ are: (Velocity of sound $=340{\text{ms}}^{-1}$)

A force $(4\hat{i}+\hat{j}-2\hat{k})\text{N}$ acting on a body maintains its velocity at $(2\hat{i}+3\hat{j}-\hat{k})\text{m/s}$. The power exerted is

The block of mass $m\text{kg}$ is being pulled by a horizontal force $F=2\text{mg}$ applied to a string as shown in figure (Take $g=10{\text{ms}}^{-2})$. The pulley is massless and is fixed at the edge of an immovable table with a supporting cable. What is the value of force exerted by the supporting cable (rod) on the pulley (in $\text{Newton}$).

A ball of mass 0.2kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2m while applying the force and the ball goes up to 2m height further, find the magnitude of force. (Consider g = 10m/s²).

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ ?

Total number of lines emitted in the infrared region when the electron de-excited from the 5th excited state to the 1st excited state will be

The energy supplied by a power plant is $40\times {10}^6\text{kWh}$. It is supplied by annihilation of matter, the mass that is annihilated is-

[Use $1\text{kWh}=36\times {10}^5\text{J}$]

In the figure, a ball of mass $m$ is tied with two strings of equal length $l$ whose other ends are connected to a rod as shown in the figure. If $T_1$ and $T_2$ are the tensions in the upper and lower strings respectively when the rod is rotated with angular velocity $\omega$, then

The r.m.s. velocity of a gas at a certain temperature is $\sqrt{2}$ times than that of the oxygen molecules at that temperature. The gas can be

A particle of mass m having a charge q enters into a circular region of radius R with velocity v directed towards the centre. The strength of magnetic field is B. Find the deviation in the path of the particle.

A small mass $m$ is transferred from the centre of a hollow sphere of mass $M$ and radius $R$ to infinity. During this process $W_1$ is the amount of work done. If instead of a hollow sphere, a solid sphere of mass $\frac{M}{2}$ and radius $\frac{R}{3}$ were there, then $W_2$ is the amount of work done. The ratio of $\frac{W_1}{W_2}$ will be

A physical quantity of the dimensions of length that can be formed out of $c$, $G$ and $$\frac{e^2}{4\pi {\epsilon }_0}$$ is [$c$ is the velocity of light, $G$ is the universal constant of gravitation and $e$ is the charge]

A ball of mass m = 1 kg, rolling without slipping, strikes a smooth vertical wall and comes back. Before the impact the velocity of the ball is $v_1$ = 10 cm/s and just after the impact $v_1$=8 cm/s. Find the loss in energy of ball during the impact.

A particle of mass $0.2\text{kg}$ is moving in one dimension under a force that delivers a constant power $0.5\text{W}$ to the particle. If the initial speed (in $\text{m/s})$ of the particle is zero, then speed in $\left(\text{m/s}\right)$ after $5\text{s}$ is

A rope is wound around a hollow cylinder of mass $3kg$ and radius $40cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30N$.