As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.

If refractive index of the material of prism is \(\sqrt{2}\), the angle \(\theta\) of prism is.

A cubic block of mass \(m\) is sliding down on an inclined plane at \(60^{\circ}\) with an acceleration of \(\frac{\mathrm{g}}{2}\), the value of coefficient of kinetic friction is

A coil of \(200\) turns and area \(0.20 \mathrm{~m}^2\) is rotated at half a revolution per second and is placed in uniform magnetic field of \(0.01 \mathrm{~T}\) perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \(\frac{2 \pi}{\beta}\) volt. The value of \(\beta\) is _______.

Match the List-I with List-II

List - I	List - II
(A) Triatomic rigid gas	(I) \(\frac{C_P}{C_V} = \frac{5}{3}\)
(B) Diatomic non-rigid gas	(II) \(\frac{C_P}{C_V} = \frac{7}{5}\)
(C) Monoatomic gas	(III) \(\frac{C_P}{C_V} = \frac{4}{3}\)
(D) Diatomic rigid ga	(IV) \(\frac{C_P}{C_V} = \frac{9}{7}\)

Choose the correct answer from the options given below :

The velocity of a particle executing simple harmonic motion along \(x\)-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7}\) s, the value of \(x\) is _____.

A particle undergoing simple harmonic motion has time dependent displacement given by \(x(t)\, = \,A\,\sin \,\frac{{\pi t}}{{90}}\). The ratio of kinetic to potential energy \(o\) the particle at \(t=210\,s\) will be

The number of air molecules per \(\mathrm{cm}^3\) increased from \(3 \times 10^{19}\) to \(12 \times 10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is \(.........\)

A copper ball of radius \(1\, cm\) and work function \(4.47\,eV\) is irradiated with ultraviolet radiation of wavelength \(2500\mathop A\limits^o \). The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is

A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(L(L \gg l)\). Both loops are coplanar and their centres coincide at point \(O\) as shown in figure. The mutual inductance of the system is.

An astronaut of mass \(m\) is working on a satellite or biting the earth at a distance \(h\) from the earth's surface. The radius of the earth is \(R\), while its mass is \(M\). The gravitational pull \(F_G\) on the astronaut is

In a photoelectric experiment, increasing the intensity of incident light :