A current carrying rectangular loop PQRS is made of uniform wire. The length \(PR = QS =5\,cm\) and \(PQ = RS =100\,cm\). If ammeter current reading changes from I to \(2 I\), the ratio of magnetic forces per unit length on the wire \(P Q\) due to wire RS in the two cases respectively \(f_{ PQ }^{ I }: f_{ PQ }^{2 I }\) is :

Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

A bullet of \(10\, {g}\), moving with velocity \(v\), collides head-on with the stationary bob of a pendulum and recoils with velocity \(100 \, {m} / {s}\). The length of the pendulum is \(0.5\, {m}\) and mass of the bob is \(1\, {kg}\). The minimum value of \(v=\) \(....{m} / {s}\) so that the pendulum describes a circle. (Assume the string to be inextensible and \({g}=10\, {m} / {s}^{2}\) )

Two sources of sound \(S_1\) and \(S_2\) produce sound waves of same frequency \(660\, Hz\). A listener is moving from source \(S_1\) towards \(S_2\) with a constant speed \(u\, m/s\) and he hears \(10\, beats/s\). The velocity of sound is \(330\, m/s\). Then, \(u\) equals ... \(m/s\)

Given below are two statements : Statement \(I\) : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement \(II\) : The refractive indices are different for different wavelengths in dispersive medium.
In the light of the above statements, choose the correct answer from the options given below :

A balloon filled with helium \(\left(32^{\circ} C \right.\) and \(1.7\; atm\).) bursts. Immediately afterwards the expansion of helium can be considered as

A thin circular ring of mass \(M\) and radius \(R\) is rotating with a constant angular velocity \(2 \; rads ^{-1}\) in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass \(m\) be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in \(rads ^{-1}\) )

A rod of mass \(‘M’\) and length \(‘2L’\) is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of \(‘m’\) are attached at distance \(‘L/2’\) from its centre on both sides, it reduces the oscillation frequency by \(20\%\). The value of ratio \(m/M\) is close to

A wire of density \(8 \times 10^3\,kg / m ^3\) is stretched between two clamps \(0.5\,m\) apart. The extension developed in the wire is \(3.2 \times 10^{-4}\,m\). If \(Y =8 \times 10^{10}\,N / m ^2\), the fundamental frequency of vibration in the wire will be \(......\,Hz\).

At \(40\,^oC\), a brass wire of \(1\, mm\) is hung from the ceiling. A small mass, \(M\) is hung from the free end of the wire. When the wire is cooled down from \(40\,^oC\) to \(20\,^oC\) it regains its original length of \(0.2\, m\). The value of \(M\) is close to ........\(kg\) (Coefficient of linear expansion and Young's modulus of brass are \(10^{-5}/^oC\) and \(10^{11}\, N/m^2\), respectively; \(g = 10\, ms^{-2}\))

The electrostatic potential in a charged spherical region of radius \(r\) varies as \(V=a r^3+b\), where \(a\) and b are constants. The total charge in the sphere of unit radius is \(\alpha \times \pi a \in_0\). The value of \(\alpha\) is _________ .

A direct current of \(4\,A\) and an alternating current of peak value \(4\,A\) flow through resistance of \(3\,\Omega\) and \(2\,\Omega\) respectively. The ratio of heat produced in the two resistances in same interval of time will be.