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A $20$ Henry inductor coil is connected to a $10$ ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature. The pressure of $A$ is twice that of $B$. Under such conditions, the density of $A$ is found to be 1.5 times the density of $B$. The ratio of molecular weight of $A$ and $B$ is

A force acts for $0.1\text{s}$ on a body of mass $5\text{kg}$, which was initially at rest. The force is then withdrawn and the body continues to move with a velocity of $2\text{m/s}$. Find the magnitude of force.

Let $\omega$ be the angular velocity of the earth’s rotation about its axis. Assume that the acceleration due to gravity on the earth’s surface has the same value at the equator and at the poles. An object weighed at the equator gives the same reading as a reading taken at a depth $d$ below earth’s surface at a pole $(d<<R)$.The value of $d$ is

A particle is projected with velocity of $u=30\hat{i}+40\hat{j}$. Its velocity after $2$ seconds is

Take $(g=10m/s^2)$

When two bodies collide elastically, then

A body of mass 2 kg is dropped from a building of height 5 m. The maximum kinetic energy the body can attain is ___ J.

An electron in a hydrogen atom first jumps from third excited state to second excited state and then from second excited state to first excited state. The ratio of wavelengths ${\lambda }_1:{\lambda }_2$ emitted in the two cases is -

A metal has a work function of $2.5\times {10}^{-19}J.$The threshold frequency beyond which photo electrons will come out is.

Energy per unit volume u is given by the relation $u=\frac{a}{b}cos\left(\frac{az}{k\theta }\right)$ where z is distance, k is Boltzmann constant, $\theta$ is temperature. Then the dimensional formula of b is

Given that sound travels in air at $340\text{m/s}$. In air, a sound source is producing a wave of wavelength $34\text{cm}$. If the same source is put in a water tank, what would be the wavelength of sound wave in water?



$[$Speed of sound in water is $1360\text{m/s}]$

Period of the function $f\left(x\right)=4\sec (3x-\frac{\pi }{4})$ is

A uniform thin rod of mass $m$ and length $R$ is placed normally on surface of earth as shown. The mass of earth is $M$ and its radius is $R$. Then the magnitude of gravitational force exerted by earth on the rod is :

In the arrangement shown in figure, the pulleys are small and light and the springs are ideal. $K_1=25{\pi }^2\text{N/m},K_2=2K_1,K_3=4K_1$ and $K_4=4K_1$ are the force constants of the springs. Calculate the period of small vertical oscillations of the block of mass $m=2\text{kg}$.

If nitrogen gas molecules goes straight up from the surface of the earth with its rms speed at $0^{\circ }\text{C}$ and there is no collision with other molecules, then it will rise to an approximate height of:

(Given, The acceleration due to gravity at a comparable height $h$ above earth's surface is given by $g^{\prime }=\frac{h}{1+\frac{h}{R}}$)

Four charges each equal to $Q$ are placed at the four corners of a square and a charge $q$ is placed at the centre of the square. If the system is in equilibrium then the value of $q$ is

The mean free path of conduction electrons in copper is about $4\times {10}^{-8}m$. For a copper block, find the electric field which can give, on an average, $1eV$ energy to a conduction electons.

A U tube is made of two capillary tubes of diameter $0.5\text{mm}$ and $1.0\text{mm}$ respectively. It contains $H_{2}O$. Find the difference in the levels of water between the two arms of the U tube. (Surface tension of $H_{2}O=75\text{dynes/cm}$ and $g=980{\text{cm/s}}^2$).

A block of mass 0.5 kg hanging from a vertical spring executes simple harmonic motion of amplitude 0.1 m and time period 0.314 s. Find the maximum force exerted by the spring on the block.

Two uniform identical rods each of mass $M$ and length $L$ are joined to form a cross as shown in the figure. Find the moment of inertia of the cross about a bisector in the plane of rods as shown by dotted line in the figure.

For a given A.C voltage $V=V_0\sin \omega t$, if $V_1$ is average voltage of half cycle and $V_2$ is rms voltage, then $\frac{V_1}{V_2}$ is

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas):-

A particle falls from a height 'h upon a fixed horizontal plane and rebounds. If 'e' is the coefficient of restitution, then the total distance travelled before rebounding has stopped is

Silver plating is carried out from which of the following?

The total current supplied to the circuit by the battery as shown in figure is

A person has near point at $100\text{cm}$. What power of lens is needed to read at $20\text{cm}.$ If he/she uses spectacles, having glasses $2\text{cm}$ separated from eyes?

A graph of the $x$ component of the electric field as a function of $x$ in a region of space is shown. The $y$ and $z$ components of the electric fields are zero in this region. If the electric potential is $10\text{V}$ at the origin, then the potential at $x=2\text{m}$ is