The current of \(5 \mathrm{~A}\) flows in a square loop of sides \(1\) \(\mathrm{m}\) is placed in air. The magnetic field at the centre of the loop is \(\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}\). The value of \(\mathrm{X}\) is _______.

A gas can be taken from \(A\) to \(B\) via two different processes \(ACB\) and \(ADB\). When path \(ACB\) is used \(60\, J\) of heat flows into the system and \(30\, J\) of work is done by the system. If path \(ADB\) is used work down by the system is \(10\, J\). the heat flow into the system in path \(ADB\) is ..... \(J\)

Two liquids of densities \(\rho_{1}\) and \(\rho_{2}\left(\rho_{2}=2 \rho_{1}\right)\) are filled up behind a square wall of side \(10\; \mathrm{m}\) as shown in figure. Each liquid has a height of \(5 \;\mathrm{m} .\) The ratio of the forces due to these liquids exerted on upper part \(MN\) to that at the lower pait \(NO\) is (Assume that the liquids are not mixing)

Two stars are \(10\) light years away from the earth. They are seen through a telescope of objective diameter \(30\, cm\). The wavelength of light is \(600\, nm\). To see the stars just resolved by the telescope, the minimum distance between them should be ( \(1\) light year \(= 9.46 \times 10^{15}\, m\)) of the order of

The vertical component of the earth's magnetic field is \(6 \times 10^{-5} T\) at any place where the angle of dip is \(37^{\circ}\). The earth's resultant magnetic field at that place will be \(\left(\right.\) Given \(\left.\tan 37^{\circ}=\frac{3}{4}\right)\)

A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)

A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) is

A heat engine operates between a cold reservoir at temperature \({T}_{2}=400\, {K}\) and a hot reservoir at temperature \({T}_{1} .\) It takes \(300 \,{J}\) of heat from the hot reservoir and delivers \(240\, {J}\) of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be \(....{K}\)

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by \(100 \,\mu A\), it brings a change of \(10 \,mA\) in collector current. If the load resistance is \(2 \,k \Omega\) and input resistance is \(1 \,k \Omega\), the value of power gain is \(x \times 10^{4}\). The value of \(x\) is_________