Light is incident normally on a completely absorbing surface with an energy flux of \(25\,W\,cm^{-2}.\) If the surface has an area of \(25\,cm^2,\) the maximum momentum transferred to the surface in \(40\,min\) time duration will be

An object of uniform density rolls up the curved path with the initial velocity \(v_0\) as shown in the figure. If the maximum height attained by an object is \(\dfrac{7v_0^2}{10g}\) (\(g\) = acceleration due to gravity), the object is a _______.

A container of fixed volume contains a gas at \(27^{\circ} \mathrm{C}\). To double the pressure of the gas, the temperature of gas should be raised to ______ \({ }^{\circ} \mathrm{C}\).

A conducting metal circular-wire-loop of radius \(r\) is placed perpendicular to a magnetic field which varies with time as \(B = {B_0}{e^{\frac{{ - t}}{\tau }}}\) , where \(B_0\) and \(\tau \) are constants, at time \(t = 0\). If the resistance of the loop is \(R\) then the heat generated in the loop after a long time \(\left( {t \to \infty } \right)\) is

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is _____.

The activity of a radioactive material is \(6.4 \times 10^{-4}\) curie. Its half life is \(5\; days\). The activity will become \(5 \times 10^{-6}\) curie after \(.......day\)

A particle is subjected two simple harmonic motions as :
\(\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}\)
and \(x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}\)
where x is displacement and \(t\) is time in seconds. The maximum acceleration of the particle is \(\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}\). The value of x is :

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is \(\sqrt{\frac{2}{x}}\). The value of \(x\) is \(.......\)

For a transistor to act as a switch, it must be operated in

Two small spherical balls of mass 10 g each with charges \(-2 \mu \mathrm{C}\) and \(2 \mu \mathrm{C}\), are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of \(100 \mu \mathrm{C} / \mathrm{m}^2\) such that length of rod makes an angle of \(30^{\circ}\) with electric field generated by charge sheet. Net torque acting on the rod is:
(Take \(\varepsilon_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\))

A string of length \(1\, m\) and mass \(5\, g\) is fixed at both ends. The tension in the string is \(8.0\, N\). The string is set into vibration using an external vibrator of frequency \(100\, Hz\). The separation between successive nodes on the string is close to .... \(cm\)

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