A string of length \(L\) is fixed at one end and carries a mass of \(M\) at the other end. The mass makes \(\left(\frac{3}{\pi}\right)\) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is \(\ldots\ldots\) ML.

The drift velocity of electrons for a conductor connected in an electrical circuit is \(V _{ d }\). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

Consider a galvanometer shunted with \(5\, \Omega\) resistance and \(2\, \%\) of current passes through it. What is the resistance of the given galvanometer? (In \(\Omega\))

The electric field in a region is given by \(\overrightarrow{\mathrm{E}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \times 10^3 \mathrm{~N} / \mathrm{C}\). The flux of the field through a rectangular surface parallel to \(x-z\) plane is \(6.0 \mathrm{Nm}^2 \mathrm{C}^{-1}\). The area of the surface is ________ \(\mathrm{cm}^2\).

Two identical blocks \(A\) and \(B\) each of mass \(m\) resting on the smooth horizontal floor are connected by a light spring of natural length \(L\) and spring constant \(K\). A third block \(C\) of mass \(m\) moving with a speed \(v\) along the line joining \(A\) and \(B\) collides with \(A\).The maximum compression in the spring is

A capacitor is made of a tlat plate of area \(A\) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is \(\mathrm{d}\), the capacitance of the arrangement is _______.

The magnetic moment of a bar magnet is \(0.5 \mathrm{Am}^2\). It is suspended in a uniform magnetic field of \(8 \times 10^{-2} \mathrm{~T}\). The work done in rotating it from its most stable to most unstable position is _______.

A uniformly tapering conical wire is made from a material of Young's modulus \(Y\)  and has a normal, unextended length \(L.\) The radii, at the upper and lower ends of this conical wire, have values \(R\) and \(3R,\)  respectively. The upper end of the wire is fixed to a rigid support and a mass \(M\) is suspended from its lower end. The equilibrium extended length, of this wire, would equal 

The temperature of a body in air falls from \(40^{\circ} \mathrm{C}\) to \(24^{\circ} \mathrm{C}\) in 4 minutes. The temperature of the air is \(16^{\circ} \mathrm{C}\). The temperature of the body in the next 4 minutes will be:

A balloon carries a total load of \(185\; {kg}\) at normal pressure and temperature of \(27^{\circ} {C}\). What load will the balloon carry on rising to a height at which the barometric pressure is \(45\; {cm}\) of \({Hg}\) and the temperature is \(-7^{\circ} {C}\). Assuming the volume constant? (in \({kg}\))

A \(2\,V\) battery is connected across \(AB\) as shown in the figure. The value of the current supplied by the battery when in one case battery's positive terminal is connected to \(A\) and in other case when positive terminal of battery is connected to \(B\) will respectively be