A tuning fork resonates with a sonometer wire of length \(1 \mathrm{~m}\) stretched with a tension of \(6 \mathrm{~N}\). When the tension in the wire is changed to \(54 \mathrm{~N}\), the same tuning fork produces \(12\) beats per second with it. The frequency of the tuning fork is _______ \(\mathrm{Hz}\).

If the maximum load carried by an elevator is \(1400\,kg\) (\(600\,kg\) - Passenger \(+800\,kg\) - elevator), which is moving up with a uniform speed of \(3\,ms ^{-1}\) and the frictional force acting on it is \(2000\,N\), then the maximum 10.Power used by the motor is \(...........\,kW \left( g =10\,m / s ^2\right)\).

Initially a satellite of 100 kg is in a circular orbit of radius \(1.5 R _{ E }\). This satellite can be moved to a circular orbit of radius \(3 R _{ E }\) by supplying \(\alpha \times 10^6 J\) of energy. The value of \(\alpha\) is _________ .
(Take Radius of Earth \(R_E=6 \times 10^6 m\) and \(g =10 m / s ^2\) )

A \(10\,m\) long horizontal wire extends from North East to South West. It is falling with a speed of \(5.0\,ms^{-1},\) at right angles to the horizontal component of the earth’s magnetic field, of \(0.3\times 10^{-4}\,Wb/m^2\). The value of the induced \(emf\) in wire is 

Match List\(-I\) with List\(-II\)

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

A \(5 \,V\) battery is connected across the points \(X\) and \(Y\). Assume \(D_{1}\) and \(D_{2}\) to be normal silicon diodes. Find the current (in \(A\)) supplied by the battery if the \(+ve\) terminal of the battery is connected to point \(X\)

A conducting circular loop is placed in a uniform magnetic field of \(0.4\,T\) with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of \(1\,mm / s\). The magnitude of induced emf in the loop at an instant when the radius of the loop is \(2\,cm\) will be \(...........\,\mu V\).

An electric dipole is placed on \({x}\)-axis in proximity to a line charge of linear charge density \(3.0 \times 10^{-6}\, {C} / {m}\). Line charge is placed on \(z-\)axis and positive and negative charge of dipole is at a distance of \(10\, {mm}\) and \(12\, {mm}\) from the origin respectively. If total force of \(4\, {N}\) is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

Two massless springs with spring constants \(2\,k\) and \(9\,k\), carry \(50\, g\) and \(100 \,g\) masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be

The approximate height from the surface of earth at which the weight of the body becomes \(\frac{1}{3}\) of its weight on the surface of earth is \(..........km\) : [Radius of earth \(R =6400 \,km\) and \(\sqrt{3}=1.732]\)

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is \(1 : 4\). What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass \(2 \mathrm{~kg}\) is : _______.

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are \(Y_{1}\) and \(Y_{2}\). The combination behaves as a single wire then its Young's modulus is: