An AC source given by \(V=V_m\sin\omega t\) is connected to a pure inductor \(L\) in a circuit and \(I_m\) is the peak value of the AC current. The instantaneous power supplied to the inductor is:
1. \(\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
2. \(-\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\)
3. \({V_mI_m}\mathrm{sin}^{2}(\omega t)\)
4. \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\)
The fraction of the original number of radioactive atoms that disintegrates (decays) during the average lifetime of a radioactive substance will be:
1. \(\frac{1}{e}\)
2. \(\frac{1}{1+e}\)
3. \(\frac{e-1}{e+1}\)
4. \(\frac{e-1}{e}\)
The figure given below shows the displacement and time, \((x\text -t)\) graph of a particle moving along a straight line:
The correct statement, about the motion of the particle, is:
1. | the particle moves at a constant velocity up to a time \(t_0\) and then stops. |
2. | the particle is accelerated throughout its motion. |
3. | the particle is accelerated continuously for time \(t_0\) then moves with constant velocity. |
4. | the particle is at rest. |
Air is pushed carefully into a soap bubble of radius \(r\) to double its radius. If the surface tension of the soap solution is \(T,\) then work done in the process is:
1. | \(12\pi r^2T\) | 2. | \(24\pi r^2T\) |
3. | \(4\pi r^2T\) | 4. | \(8\pi r^2T\) |
Statement I: | The magnetic field of a circular loop at very far away point on the axial line varies with distance as like that of a magnetic dipole. |
Statement II: | The magnetic field due to magnetic dipole varies inversely with the square of the distance from the centre on the axial line. |
1. | Statement I is correct and Statement II is incorrect. |
2. | Statement I is incorrect and Statement II is correct. |
3. | Both Statement I and Statement II are correct. |
4. | Both Statement I and Statement II are incorrect. |
When a particle with charge \(+q\) is thrown with an initial velocity \(v\) towards another stationary change \(+Q,\) it is repelled back after reaching the nearest distance \(r\) from \(+Q.\) The closest distance that it can reach if it is thrown with an initial velocity \(2v,\) is:
1. | \(\dfrac{r}{4}\) | 2. | \(\dfrac{r}{2}\) |
3. | \(\dfrac{r}{16}\) | 4. | \(\dfrac{r}{8}\) |
The determination of the value of acceleration due to gravity \((g)\) by simple pendulum method employs the formula,
\(g=4\pi^2\frac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
1. | \(\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)\) | 2. | \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]\) |
3. | \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]\) | 4. | \(\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)\) |
A monochromatic light of frequency \(500\) THz is incident on the slits of a Young's double slit experiment. If the distance between the slits is \(0.2\) mm and the screen is placed at a distance \(1\) m from the slits, the width of \(10\) fringes will be:
1. \(1.5\) mm
2. \(15\) mm
3. \(30\) mm
4. \(3\) mm
In a meter bridge experiment, the null point is at a distance of \(30~\text{cm}\) from \(\mathrm{A}\). If a resistance of \(16~\Omega\) is connected in parallel with resistance \(Y\), the null point occurs at \(50~\text{cm}\) from \(\mathrm{A}\). The value of the resistance \(Y\) is:
1. | \(\dfrac{112}{3}~\Omega\) | 2. | \(\dfrac{40}{3}~\Omega\) |
3. | \(\dfrac{64}{3}~\Omega\) | 4. | \(\dfrac{48}{3}~\Omega\) |
The temperature at which the rms speed of atoms in neon gas is equal to the rms speed of hydrogen molecules at \(15^{\circ} \mathrm{C}\) is: (Atomic mass of neon \(=20.2\) u, molecular mass of hydrogen \(=2\) u)
1. | \(2.9\times10^{3}\) K | 2. | \(2.9\) K |
3. | \(0.15\times10^{3}\) K | 4. | \(0.29\times10^{3}\) K |