A magnetic field $4 \times 10^{-2} \mathrm{~T}$ acts at right angles to a coil of area $100 \mathrm{~cm}^2$ with 50 turns. The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time ' $t$ '. The value of ' $t$ ' is

A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ( $\mathrm{g}=$ acceleration due to gravity)

A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns is

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