The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability \(\mu=2\mu_{0}\), is
( \(\mu_0=\) permeability of vacuum)

In the given figure, the block of mass \(m\) is dropped from the point ' \(A\) '. The expression for kinetic energy of block when it reaches point ' \(B\) ' is ................

Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

The root mean square velocity of molecules of gas is

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.

A parallel plate capacitor with plate separation \(5\) \(\mathrm{mm}\) is charged up by a battery. It is found that on introducing a dielectric sheet of thickness \(2 \mathrm{~mm}\), while keeping the battery connections intact, the capacitor draws \(25 \%\) more charge from the battery than before. The dielectric constant of the sheet is _______.

Four identical discs each of mass ' \(M\) ' and diameter ' \(a\) ' are arranged in a small plane as shown in figure. If the moment of inertia of the system about \(OO ^{\prime}\) is \(\frac{ x }{4} Ma ^{2}\). Then, the value of \(x\) will be \(......\)

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 :

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )