Dimension of \(\frac{1}{\mu_0 \varepsilon_0}\) should be equal to

Consider two identical springs each of spring constant \(k\) and negligible mass compared to the mass \(M\) as shown. Fig. \(1\) shows one of them and Fig. \(2\) shows their series combination. The ratios of time period of oscillation of the two \(SHM\) is \(\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },\) where value of \(x\) is (Round off to the Nearest Integer)

Correct formula for height of a satellite from earths surface is _______.

For a body executing \(S.H.M. :\) \((a)\) Potential energy is always equal to its \(K.E.\) \((b)\) Average potential and kinetic energy over any given time interval are always equal. \((c)\) Sum of the kinetic and potential energy at any point of time is constant. \((d)\) Average \(K.E.\) in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below:

The current in a conductor is expressed as \(I=3 t^2+4 t^3\), where \(I\) is in Ampere and \(t\) is in second. The amount of electric charge that flows through a section of the conductor during \(t=1\) s to \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\).

An electromagnetic wave of frequency \(1\times10^{14}\, hertz\) is propagating along \(z-\) axis. The amplitude of electric field is \(4\, V/m\) . lf \({\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2\) , then average energy density of electric field will be:

When one light ray is reflected from a plane mirror with \(30^{\circ}\) angle of reflection, the angle of deviation of the ray after reflection is \(.....^{\circ}\)

The equivalent resistance between \(A\) and \(B\) of the network shown in figure

A small circular loop of conducting wire has radius \(a\) and carries current \(I\). It is placed in a uniform magnetic field \(\mathrm{B}\) perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period \(T\). If the mass of the loop is \(m\) then 

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

There are \(10^{10}\) radioactive nuclei in a given radioactive element, Its half-life time is \(1\, minute.\) How many nuclei will remain after \(30\, seconds?\) \((\sqrt{2}=1.414)\)