A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with \(3 m / s ^2\). At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is \(5 m / s\). The initial height of the aeroplane is ___________m.
\(\left( g =10 m / s ^2\right)\)

The magnetic moment of an electron \((e)\) revolving in an orbit around nucleus with an orbital angular momentum is given by :

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \(\tau_{1}\) to \(\tau_{2} .\) If \(\frac{C_{p}}{C_{v}}=\gamma\) for this gas then a good estimate for \(\frac{\tau_{2}}{\tau_{1}}\) is given by :

One end of a straight uniform \(1\; \mathrm{m}\) long bar is pivoted on horizontal table. It is released from rest when it makes an angle \(30^{\circ}\) from the horizontal (see figure). Its angular speed when it hits the table is given as \(\sqrt{\mathrm{n}}\; \mathrm{s}^{-1},\) where \(\mathrm{n}\) is an integer. The value of \(n\) is

In the reported figure, there is a cyclic process \(ABCDA\) on a sample of \(1\, {mol}\) of a diatomic gas. The temperature of the gas during the process \({A} \rightarrow {B}\) and \({C} \rightarrow {D}\) are \({T}_{1}\) and \({T}_{2}\left({T}_{1}\,>\,{T}_{2}\right)\) respectively. Choose the correct option out of the following for work done if processes \(B C\) and \(D A\) are adiabatic.

The number of molecules in one litre of an ideal gas at \(300 \,{K}\) and \(2\) atmospheric pressure with mean kinetic energy \(2 \times 10^{-9}\, {J}\) per molecules is \(....\, \times 10^{11}\)

Photons of an electromagnetic radiation has an energy \(11\, keV\) each. To which region of electromagnetic spectrum does it belong ?

The energy of an electron in an orbit of the Bohr's atom is \(-0.04 E _0 eV\) where \(E _0\) is the ground state energy. If \(L\) is the angular momentum of the electron in this orbit and h is the Planck's constant, then \(\frac{2 \pi L}{ h }\) is _________ :

Consider two charged metallic spheres \(S_{1}\) and \(\mathrm{S}_{2}\) of radii \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2},\) respectively. The electric \(\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)\) on their surfaces are such that \(\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .\) Then the ratio \(\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)\) of the electrostatic potentials on each sphere is 

A mercury drop of radius \(10^{-3}\,m\) is broken into \(125\) equal size droplets. Surface tension of mercury is \(0.45\,Nm ^{-1}\). The gain in surface energy is \(......\times 10^{-5}\,J\)