Physics

The X-Y plane be taken as the boundary between two transparent media M₁ and M₂. M₁ in $z\ge 0$  has a refractive index of $\sqrt[]{2}$  and M₂ with Z < 0 has refractive index of $\sqrt[]{3}.$ A ray of light travelling in M₁ along the direction given by the vector $\overrightarrow{P}=4\sqrt[]{3}\widehat{i}-3\sqrt[]{3}\widehat{j}-5\widehat{k},$  is incident on the plane of separation. The value of difference between the angle of incident in M₁ and the angle of refraction in M₂ will be_______ degree.

A wire of length 314cm carrying current of 14A is bent to form a circle. The magnetic moment of the coil is_________ A -m². [Given π = 3.14]

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is . The difference of resultant intensities, at the point A and B, will be_________I.

A closely wounded circular coil of radius 5cm produces a magnetic field of 37.68 * 104 T at its centre. The current through the coil is_ A. [Given, number of turns in the coil is 100 and = 3.14]

The current I flowing through the given circuit will be_________A.

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture of constant volume is $\frac{{\alpha }^2}{4}RJ/molK;$ then the value of will be________.

(Assume that the given diatomic gas has no vibrational mode.)

The pressure P1 and density d1 of diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes suddenly to P2(>P1) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given $\frac{d_2}{d_1}=32)$

The pressure P1 and density d1 of diatomic gas $\left(\gamma =\frac{7}{5}\right)$ changes suddenly to P2(>P1) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given $\frac{d_2}{d_1}=32)$

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a dept ah(h <e) from the earth surface. The value of a will be_______.

An object is projected in the air with initial velocity u at an angle q. The projectile motion is such that the horizontal range R, in maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be_______degree.