A body is released from a height equal to the radius ( \(R\) ) of the earth. The velocity of the body when it strikes the surface of the earth will be : (Given \(g\) = acceleration due to gravity on the earth.)

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.

A uniform metal chain of mass \(m\) and length ' \(L\) ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' \(l\) ' is hanging on one side and rest of its length ' \(L -l\) ' is hanging on the other side of the pulley. At a certain point of time, when \(l=\frac{L}{x}\), the acceleration of the chain is \(\frac{g}{2}\). The value of \(x\) is ........

The \(AC\) voltage across a resistance can be measured using a

The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8\  \Omega\) varies with time (in seconds) as \(\phi=5 t^2-36 t+1\). The induced current in the circuit at \(t=2 \mathrm{~s}\) is _______ \(\mathrm{A}\).

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

The area of cross-section of a railway track is \(0.01\, {m}^{2}\). The temperature variation is \(10^{\circ} {C}\). Coefficient of linear expansion of material of track is \(10^{-5} /{ }^{\circ} {C}\). The energy stored per meter in the track is ...... \({J} / {m} .\) (Young's modulus of material of track is \(10^{11} \,{Nm}^{-2}\) ))

At steady state the charge on the capacitor, as shown in the circuit below, is _________ \(\mu \mathrm{C}\).

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours \(30\) minutes.

The mass defect in a particular reaction is \(0.4 \mathrm{~g}\). The amount of energy liberated is \(\mathrm{n} \times 10^7 \mathrm{kWh}\), where\(\mathrm{n}=\)________. (speed of light \(=3 \times 10^8 \mathrm{~m} / \mathrm{s}\) )

There is a small source of light at some depth below the surface of water (refractive index \(=\frac{4}{3}\) ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly)...........\(\%\) [Use the fact that surface area of a spherical cap of height \(\mathrm{h}\) and radius of curvature \(\mathrm{r} \text { is } 2 \pi \mathrm{rh}]\)