Velocity-time graph for a body of mass \(10\, kg\) is shown in figure. Work-done on the body in first two seconds of the motion is  ................ \(\mathrm{J}\)

A vernier callipers has \(20\) divisions on the vernier scale, which coincides with \(19^{\text {th }}\) division on the main scale. The least count of the instrument is \(0.1 \mathrm{~mm}\). One main scale division is equal to _______ \(\mathrm{mm}\).

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ...........

An ac circuit has an inductor and a resistor of resistance \({R}\) in series, such that \({X}_{{L}}=3 {R}\). Now, a capacitor is added in series such that \({X}_{{C}}=2 {R}\). The ratio of new power factor with the old power factor of the circuit is \(\sqrt{5}: {x}\). The value of \({x}\) is ...... .

Two \(10 \; cm\) long, straight wires, each carrying a current of \(5 \; A\) are kept parallel to each other. If each wire experienced a force of \(10^{-5} \; N\), then separation between the wires is \(\dots \; cm\).

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(S\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of 1 m from \(S\) and has a speed of \(1 m s ^{-1}\). The maximum value of \(\sigma\), if the electron strikes \(S\) at \(t=1 s\) is \(\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{ C }{ m ^2}\). The value of \(\alpha\) is __________ .

A \(25\,cm\) long solenoid has radius \(2\,cm\) and \(500\) total number of turns. It carries a current of \(15\,A.\) If it is equivalent to a magnet of the same size and magnetization \(\vec M\) ( magnetic moment/ volume), then \(\left| {\vec M} \right|\)  is

A \(12.5\, eV\) electron beam is used to bombard gaseous hydrogen at room temperature. It will emit

A source supplies heat to a system at the rate of \(1000 \,W\). If the system performs work at a rate of \(200\,W\). The rate at which internal energy of the system increases \(.......\,W\)