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A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle, of ${75}^{\circ }$. One of the fields has a magnitude of $\sqrt{2}\times {10}^{-2}T$. The dipole attains stable equilibrium at an angle of ${30}^{\circ }$ with this field. What is the magnitude of the other field?

A string is clamped at both the ends and it is vibrating in its
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$4^{\text{th}}$ harmonic. The equation of the stationary wave is $Y=0.3\sin \left(0.157x\right)\cos \left(200\pi t\right).$ The length of the string is

(All quantities are in SI units.)

An electormagnetic flow meter is used to measure the average flow rate of an effluent in a pipe of diameter $40mm$. The velocity profile is symmetrical and can be assumed unifrom. The flux density in the liquid has a peak value of $0.2Wb/m^2$. If the output from the flowmeter electrode is recorder as $0.4V$ peak to peak. Then the average velocity of the effluent in the pipe is ____ $m/sec$

The permeability of a material is $628\times {10}^{-6}\text{SI unit}$. Its magnetic susceptibility will be -



Take, ${\mu }_o=4\pi \times {10}^{-7}\text{SI unit}$

A particle is projected with a velocity $v$ such that its range on horizontal plane is twice the greatest height attained by it. The range of the projectile will be ($g$ is the acceleration due to gravity).

The height of a mercury column in a barometer in a Calcutta library was recorded to be 75cm.Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = 13.6,Density of water = 10³ kg/m³,g = 9.8 m/s² at Calcutta .Pressure = hpg in usual symbols.

If the equation for the angular displacement of a particle moving on a circular path is given by $\theta =2t^3+0.5$, where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle at $2\text{s}$ is

Estimate the distance
for which ray optics is good approximation for an aperture of 4 mm
and wavelength 400 nm.

For the given electric field lines configuration of two charges, the value of the angle $\theta$ is

Suppose a light wave has wavelength $\left(\lambda \right)$, frequency $\left(\nu \right)$ and speed $\left(c\right)$ in the air $({\mu }_a=1)$ . It passes through a medium with refractive index $\left(\mu \right)$. The modified wavelength, frequency and speed would be-

Simplify:$\frac{sin\alpha }{(1+cos\alpha )}+\frac{(1+cos\alpha )}{sin\alpha }$

The displacement-time$(x-t)$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=\frac{4}{3}\text{s}$ is

A capacitor of capacitance $C$ is charged to a potential difference $V$ from a cell and then disconnected from it. A charge $+Q$ is now given to its positive plate. The potential difference across the capacitor is now

1. 7.7

A gaseous mixture enclosed in a vessel consists of one $\text{gram mole}$ of a gas $A$ with $\gamma =\frac{5}{3}$ and some amount of gas $B$ with $\gamma =\frac{7}{5}$ at a temperature $T$. The gases $A$ and $B$ do not react with each other and are assumed to be ideal. Find the number of moles of the gas $B$ if $\gamma$ for the gaseous mixture is $\left(\frac{19}{13}\right)$.

1. 3242.4

In the figure shown, what is the apparent distance of the bird as seen by the fish ?

A
rectangular wire loop of sides 8 cm and 2 cm with a small cut is
moving out of a region of uniform magnetic field of magnitude 0.3 T
directed normal to the loop. What is the emf developed across the cut
if the velocity of the loop is 1 cm s⁻¹
in a direction normal to the (a) longer side, (b) shorter side of the
loop? For how long does the induced voltage last in each case?

In the circuit shown in the figure, the input voltage are $V_C=15V$ and $V_B=10V$. The value of $I_B,I_C$ and $\beta$ respectively is (Assume that the collector and base voltages are negligible.)

Five point charges $(+q$ each$)$ are placed at the five vertices of a regular hexagon of side $2a$. What is the magnitude of the net electric field at the centre of the hexagon?

The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of ${15}^{\circ }$ with the horizontal is

Express $L$ (length) in terms of $G,h$ and $c$ -

Here $G$ is universal gravitational constsnt, $h$ is plank's constant, $c$ is speed of light

In Davisson-German experiment, observed value of de-Broglie’s wavelength is 0.165$nm$ whereas theoretical value is 0.166$nm$. Choose the correct reason for lower experimental value.

A long solenoid has 200 turns per cm and carries a current of 2.5 amps. The magnetic field at its centre is (${\mu }_0=4\pi \times {10}^{-7}weber/amp-m$)

A body cools from ${50}^{\circ }C$ to ${40}^{\circ }C$ in $5$ minutes. The surrounding temperature is ${20}^{\circ }C$. In what further time (in minutes) will it cool to ${30}^{\circ }C$