A liquid drop having \(6\) excess electrons is kept stationary under a uniform electric field of \(25.5\, k\,Vm^{-1}\) . The density of liquid is \(1.26\times10^3\, kg\, m^{-3}\) . The radius of the drop is (neglect buoyancy)

The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth.

Take the mean distance of the moon and the sun from the earth to be \(0.4 \times 10^6\,km\) and \(150 \times 10^6\,km\) respectively. Their masses are \(8 \times 10^{22}\, kg\) and \(2 \times 10^{30}\, kg\) respectively. The radius of the earth is \(6400\, km\). Let \(\Delta {F_1}\) be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and \(\Delta {F_2}\) be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to \(\frac{{\Delta {F_1}}}{{\Delta {F_2}}}\) is

In Young's double slit experiment the two slits are \(0.6 \; mm\) distance apart. Interference pattern is observed on a screen at a distance \(80 \; cm\) from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be \(\dots \; nm .\)

A uniform rod of mass m and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _________.(g acceleration due to gravity)

A disc with a flat small bottom beaker placed on it at a distance \(R\) from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if 

A wire of length \(L\) is hanging from a fixed support. The length changes to \(L _{1}\) and \(L _{2}\) when masses \(1 \,kg\) and \(2 \,kg\) are suspended respectively from its free end. Then the value of \(L\) is equal to ..................

The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\)

If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of

An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).