The area of cross-section of a railway track is \(0.01\, {m}^{2}\). The temperature variation is \(10^{\circ} {C}\). Coefficient of linear expansion of material of track is \(10^{-5} /{ }^{\circ} {C}\). The energy stored per meter in the track is ...... \({J} / {m} .\) (Young's modulus of material of track is \(10^{11} \,{Nm}^{-2}\) ))

A small ball of mass \(m\) and density \(\rho\) is dropped in a viscous liquid of density \(\rho_0\). After sometime, the ball falls with constant velocity. The viscous force on the ball is _______.

A paramagnetic sample shows a net magnetisation of \(6 \,A / m\) when it is placed in an external magnetic field of \(0.4 \,T\) at a temperature of \(4\, K\). When the sample is placed in an external magnetic field of \(0.3\, T\) at a temperature of \(24\, K\), then the magnetisation will be\(......A/m\)

In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm . Total magnification obtained with this system for normal adjustment is \((5)^{ k }\). The value of k is _________

A particle of mass \(M\) is moving in a circle of fixed radius \(R\) in such a way that its centripetal acceleration at time \(t\) is given by \(n^2Rt^2\) where \(n\) is a constant. The Power delivered to the particle by the force acting on it, is

The electrostatic potential on the surface of uniformly charged spherical shell of radius \(\mathrm{R}=10 \mathrm{~cm}\) is 120 V. The potential at the centre of shell, at a distance \(\mathrm{r}=5 \mathrm{~cm}\) from centre, and at a distance \(\mathrm{r}=15 \mathrm{~cm}\) from the centre of the shell respectively, are :

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

A simple pendulum is being used to determine the value of gravitational acceleration \(\mathrm{g}\) at a certain place. The length of the pendulum is \(25.0\; \mathrm{cm}\) and a stop watch with \(1\; \mathrm{s}\) resolution measures the time taken for \(40\) oscillations to be \(50\; s\). The accuracy in \(g\) is  ....... \(\%\)

Two particles are located at equal distance from origin. The position vectors of those are represented by \(\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}\) and \(\bar{B}=2 \hat{i}-2 \hat{j}+4 p \hat{k}\), respectively. If both the vectors are at right angle to each other, the value of \(\mathrm{n}^{-1}\) is _____ .

A spaceship of mass \(2 \times 10^4\,kg\) is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be \(......\) (if \(g =10\,m / s ^2\) and radius of earth \(=6400\,km\) )

A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north . Neutral points are found at a distance of \(30\, cm\) from the magnet on the East - West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in \(Am^2\) is close to: (Given \(\frac{{{\mu _0}}}{{4\pi }}\, = 10^{- 7}\) in \(SI\,units\) and \(B_H\, =\) Horizontal component field \(= 3.6\times10^{-5}\, tesla\))