Temperature difference of \(120\,^oC\) is maintained between two ends of a uniform rod \(AB\) of length \(2L\). Another bent rod \(PQ\), of same cross-section as \(AB\) and length \(\frac{{3L}}{2}\),  is connected across \(AB\) (See figure). In steady state, temperature difference between \(P\) and \(Q\) will be close to .......... \(^oC\)

The centre of a wheel rolling on a plane surface moves with a speed \(v_{0} .\) A particle on the rim of the wheel at the same level as the centre will be moving at a speed \(\sqrt{x}\, v_{0}\). Then the value of \(x\) is ...... .

The boxes of masses \(2\, {kg}\) and \(8\, {kg}\) are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass \(8\; {kg}\) to strike the ground starting from rest. (use \(\left.{g}=10\, {m} / {s}^{2}\right)\) (in \({s}\))

The function of time representing a simple harmonic motion with a period of \(\frac{\pi}{\omega}\) is :

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is.

Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surfface is\(.......eV\) (Plancks constant \(\left. h =6.62 \times 10^{-34}\, J . s \right)\)

A resistance is shown in the figure. Its value and tolerance are given respectively by

Two wires \(W_1\) and \(W_2\) have the same radius \(r\) and respective densities \({\rho _1}\) and \({\rho _2}\) such that \({\rho _2} = 4{\rho _1}\). They are joined together at the point \(O\), as  shown in the figure. The combination is used as a sonometer wire and kept under tension \(T\). The point \(O\) is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of an tin odes formed in \(W_1\) to \(W_2\) is

A solid sphere of radius \(R\) carries a charge \((Q+q)\) distributed uniformly over its volume. A very small point like piece of it of mass \(m\) gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge \(q.\) If it acquires a speed \(v\) when it has fallen through a vertical height \(y\) (see figure), then : (assume the remaining portion to be spherical).

The electrostatic potential on the surface of uniformly charged spherical shell of radius \(\mathrm{R}=10 \mathrm{~cm}\) is 120 V. The potential at the centre of shell, at a distance \(\mathrm{r}=5 \mathrm{~cm}\) from centre, and at a distance \(\mathrm{r}=15 \mathrm{~cm}\) from the centre of the shell respectively, are :