The electric current through a wire varies with time as \(I=I_0+\beta t\). where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

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 ...... .

If \({q}_{{f}}\) is the free charge on the capacitor plates and \({q}_{{b}}\) is the bound charge on the dielectric slab of dielectric constant \(k\) placed between the capacitor plates, then bound charge \(q_{b}\) can be expressed as 

An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is: __________ .

Nucleus A is having mass number \(220\) and its binding energy per nucleon is \(5.6 \,MeV\). It splits in two fragments '\(B\)' and '\(C\)' of mass numbers \(105\) and \(115\) The binding energy of nucleons in '\(B\)' and '\(C\) ' is \(6.4 \,MeV\) per nucleon. The energy \(Q\) released per fission will be............\(MeV\)

The maximum speed of a boat in still water is \(27 \mathrm{~km} / \mathrm{h}\). Now this boat is moving downstream in a river flowing at \(9 \mathrm{~km} / \mathrm{h}\). A man in the boat throws a ball vertically upwards with speed of \(10 \mathrm{~m} / \mathrm{s}\). Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))

A copper rod of mass \(m\) slides under gravity on two smooth parallel rails, with separation \(l\) and set at an angle of \(\theta\) with the horizontal. At the bottom, rails are joined by a resistance \(R\). There is a uniform magnetic field \(B\) normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\frac{\pi}{2}\) at point \(P\) and \(\pi\) at point \(Q\). Then the difference between the resultant intensities at \(P\) and \(Q\) will be.......\(I\)

The de Broglie wavelength of a proton and \(\alpha\) -particle are equal. The ratio of their velocities is ...... .