A transformer has an efficiency of \(80 \%\) and works at \(10 \mathrm{~V}\) and \(4 \mathrm{~kW}\). If the secondary voltage is \(240 \mathrm{~V}\), then the current in the secondary coil is _______.

Two bodies of masses \(1\, kg\) and \(4\, kg\) are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency \(25\, rad/s\), and amplitude \(1.6\, cm\) while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... \(N\) ( take \(g = 10\, ms^{-2}\))

The planet Mars has two moons, if one of them has a period \(7\, hours,\, 30\, minutes\) and an orbital radius of \(9.0 \times 10^{3}\, {km} .\) Find the mass of Mars. \(\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}\)

A body of mass 2 kg moving with velocity of \(\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}\) enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \(\frac{5}{3}\) seconds, then velocity of the body when it emerges from force field is

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg , moving in opposite directions with speeds of \(10 m / s\) and \(30 m / s\), respectively, strike each other and stick together. The rise in temperature (in \({ }^{\circ} C\) ), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material \(31 cal / kg .{ }^{\circ} C\) and \(1 cal =4.2 J)\)

Given below are two statements: one is labelled a Assertion \((A)\) and the other is labelled as Reason\((R)\) \(Assertion\) \((A)\) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. \(Reason\) \((R)\) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below 

A uniform wire of length \(l\) and radius \(r\) has a resistance of \(100\, \Omega \). It is recast into a wire of radius \(\frac{r}{2}\). The resistance of new wire will be ............... \(\Omega\)

A particle of mass \( m\) moving in the \(x\) direction with speed \(2v\) is hit by another particle of mass \(2m\) moving in the \(y\) direction with speed \(v\). If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to .............. \(\%\)

The velocity of upper layer of water in a river is \(36 kmh ^{-1}\). Shearing stress between horizontal layers of water is \(10^{-3} Nm ^{-2}\). Depth of the river is \(m\). (Co-efficiency of viscosity of water is \(10^{-2} \,Pa . s\) )

In young's double slit experiment performed using a monochromatic light of wavelength \(\lambda\), when a glass plate \((\mu=1.5)\) of thickness \(x \lambda\) is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of \(x\) will be..........

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is ................

A closed organ pipe \(150 \mathrm{~cm}\) long gives \(7\) beats per second with an open organ pipe of length \(350 \mathrm{~cm}\), both vibrating in fundamental mode. The velocity of sound is_________ \(\mathrm{m} / \mathrm{s}\).