The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity)

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) )

A uniform thin metal plate of mass \(10 \mathrm{~kg}\) with dimensions is shown. The ratio of \(x\) and \(y\) coordinates of center of mass of plate in \(\frac{n}{9}\). The value of \(n\) is _______.

The least count of the main scale of a vernier callipers is \(1\, mm\). Its vernier scale is divided into \(10\) divisions and coincide with \(9\) divisions of the main scale. When jaws are touching each other, the \(7\) th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between \(3.1\, cm\) and \(3.2\, cm\) and \(4^{th}\) \(VSD\) coincides with a main scale division.The length of the cylinder is \(.....cm\) (\(VSD\) is vernier scale division)

In the given circuit the value of \(\left|\frac{I_1+I_3}{I_2}\right|\) is

A parallel plate capacitor of capacitance \(90\ pF\) is connected to a battery of \(emf\) \(20\ V\). If a dielectric material of dielectric constant \(K = \frac{5}{3}\) is inserted between the plates, the magnitude of the induced charge will be.......\(n \) \(C\)

As per the given figure, a small ball \(P\) slides down the quadrant of a circle and hits the other ball \(Q\) of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball \(Q\) after collision will be \(............\,m/s\) \(:\left( g =10\,m / s ^2\right)\)

A conducting loop of radius \(\frac{10}{\sqrt{\pi}}\,cm\) is placed perpendicular to a uniform magnetic field of \(0.5\,T\). The magnetic field is decreased to \(zero\) in \(0.5\,s\) at a steady rate. The induced emf in the circular loop at \(0.25\,s\) is:

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by \(E _{ x }= E _0 \sin ( kz -\omega t )\) \(B _{ y }= B _0 \sin ( kz -\omega t )\) Then the correct relation between \(E_0\) and \(B_0\) is given by