A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $8:1.$ The ratio of radii of the fragments is.

A condenser is charged using a constant current. The ratio of the magnetic field at a distance of $\frac{R}{2}$ and $R$ from the axis of condenser ($R$ is the radius of plate) while charging is

An infinite number of identical capacitors each of capacitance $1\mu F$ are connected $1\mu F$ are connected as shown in Fig. Then the equivalent capacitance between $A$ and $B$ is

A speech signal of $3kHz$ is used to modulate a carrier signal of frequency $1MHz$, using amplitude modulation. The frequencies of the side bands will be

Ratio of debroglie wavelengths of uncharged particle of mass m at ${27}^{0}C$ to ${127}^{0}C$ is nearly

The magnetic flux $\varphi$ (in weber ) in a closed circuit of resistance 10$\Omega$ varies with time t (in secnod) according to equation $\varphi =6t^2-5T+1.$ The magnitude of induced current at $t=0.25$ s is

A proton enters a magnetic field with a velocity of $2.5\times {10}^{7}m{s}^{-1}$ making an angle ${30}^{\circ }$ with the magnetic field. The force on the proton is $\left(B=25T\right)$

In an electromagnetic wave, the amplitude of electric firld is $1\frac{V}{m}.$ The frequency of wave is $5\times {10}^{14}Hz.$ The wave is propagating along $z-axis.$ The average energy density of electric field, in $\text{joule}/m^3,will$ be

A parallel plate capacitor of plate separation $2mm$ is connected in an electric circuit having source voltage $400V.$ If the plate area is $60c{m}^2$, then the value of displacement current for ${10}^{-6}\sec$ will be

The ratio of the magnetic field at the centre of a current carrying coil of the radius $a$ and at distance ${}^{\prime }{a}^{\prime }$ from centre of the coil and perpendicular to the axis of coil is