The value of unknown resistance \((x)\) for which the potential difference between \(B\) and \(D\) will be zero in the arrangement shown, is _______.

The temperature of a gas is \(-78^{\circ} \mathrm{C}\) and the average translational kinetic energy of its molecules is \(\mathrm{K}\). The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \(2 \mathrm{~K}\) is _______.

The distance between two consecutive points with phase difference of \(60^{\circ}\) in a wave of frequency \(500\,Hz\) is \(6.0\,m\). The velocity with which wave is traveling is \(.........km / s\)

The displacement and the increase in the velocity of a moving particle in the time interval of \(t\) to \((t+1) \mathrm{s}\) are \(125 \mathrm{~m}\) and \(50 \mathrm{~m} / \mathrm{s}\), respectively. The distance travelled by the particle in \((\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}\) is __________ \(\mathrm{m}\).

In simple harmonic motion, the total mechanical energy of given system is E. If mass of oscillating particle \(P\) is doubled then the new energy of the system for same amplitude is _______.

A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
(\(\pi = 3.14\))

Three capacitors each of \(4\,\,\mu F\)  are to be connected in such a way that the effective capacitance is \(6\,\,\mu F.\)  This can be done by connecting thern

A man of \(60\,kg\) is running on the road and suddenly jumps into a stationary trolly car of mass \(120\,kg\). Then. the trolly car starts moving with velocity \(2\,ms ^{-1}\). The velocity of the running man was _________\(ms ^{-1}\). when he jumps into the car

A uniform sphere of weight \(W\) and radius \(5\, cm\) is being held by a string as shown in the figure. The tension in the string will be

A \(60\; HP\) electric motor lifts an elevator having a maximum total load capacity of \(2000\; \mathrm{kg}\). If the frictional force on the elevator is \(4000 \;\mathrm{N}\). the speed of the elevator at full load is close to ..............  \(\mathrm{m} / \mathrm{s}\) \(\left(1 \;\mathrm{HP}=746 \;\mathrm{W}, \mathrm{g}=10\; \mathrm{ms}^{-2}\right)\)

N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity \(\omega\) as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, \(I_A-I_B\), for the given Amperian loops is:

A body is moving unidirectionally under the influence of a constant Power source. Its displacement in time \(t\) is proportional to _______.