A coil of ' $n$ ' turns and resistance $R \Omega$ is connected in series with a resistance $\frac{R}{2}$. The combination is moved for time ' $t$ ' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is

An electron of mass ' $m$ ' and charge ' $e$ ' initially at rest gets accelerated by a constant electric field ' E '. The rate of change of de-Broglie wavelength of the electron at time ' $t$ ' is

(Ignore relativistic effect)( $\mathrm{h}=$ Planck's constant)

The moment of inertia of a solid sphere of mass ' $m$ ' and radius ' $R$ ' about its diametric axis is ' $I$ '. Its moment of inertia about a tangent in the plane is

A glass cube of length 21 cm has a small air bubble trapped inside. When viewed normally from the opposite face, its apparent distance is 6 cm . The refractive index of glass and the actual distance of the air bubble from the first surface respectively are