A rectangular coil of length \(0.12~\text{m}\) and width \(0.1~\text{m}\) having \(50\) turns of wire is suspended vertically in a uniform magnetic field of strength \(0.2~\text{Wb/m}^2\). The coil carries a current of \(2~\text{A}\). If the plane of the coil is inclined at an angle of \(30^{\circ}\) with the direction of the field, the torque required to keep the coil in stable equilibrium will be:
1. \(0.15~\text{N-m}\)
2. \(0.20~\text{N-m}\)
3. \(0.24~\text{N-m}\)
4. \(0.12~\text{N-m}\)
1. \(0.15~\text{N-m}\)
2. \(0.20~\text{N-m}\)
3. \(0.24~\text{N-m}\)
4. \(0.12~\text{N-m}\)
An electron moves on a straight-line path \(XY\) as shown. The \({abcd}\) is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil?
| 1. | \({abcd}\) |
| 2. | \({adcb}\) |
| 3. | The current will reverse its direction as the electron goes past the coil |
| 4. | No current included |
A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:
| 1. | The nucleus helium has more kinetic energy than the thorium nucleus |
| 2. | The helium nucleus has less momentum than the thorium nucleus |
| 3. | The helium nucleus has more momentum than the thorium nucleus |
| 4. | The helium nucleus has less kinetic energy than the thorium nucleus |
A force \(\vec{F}=\alpha \hat{i}+3 \hat{j}+6 \hat{k}\) is acting at a point \(\vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k}\). The value of \(\alpha\) for which angular momentum about the origin is conserved is:
1. \(-1\)
2. \(2\)
3. zero
4. \(1\)
A particle is executing a simple harmonic motion. Its maximum acceleration is \(\alpha\) and maximum velocity is \(\beta.\) Then its time period of vibration will be:
1. \(\dfrac {\beta^2}{\alpha^2}\)
2. \(\dfrac {\beta}{\alpha}\)
3. \(\dfrac {\beta^2}{\alpha}\)
4. \(\dfrac {2\pi \beta}{\alpha}\)
1. X-rays
2. Infrared rays
3. Ultraviolet rays
4. \(\gamma\)-rays
Light of wavelength \(500~\text{nm}\) is incident on metal with work function \(2.28~\text{eV}\). The de-Broglie wavelength of the emitted electron is:
| 1. | \(< 2.8\times 10^{-10}~\text{m} \) | 2. | \(< 2.8\times 10^{-9}~\text{m}\) |
| 3. | \(\geq 2.8\times 10^{-9}~\text{m}\) | 4. | \(\leq 2.8\times 10^{-12}~\text{m}\) |
At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen’s wavelet from the edge of the slit and the wavelet from the midpoint of the slit is:
| 1. | \(\dfrac{\pi}{4}~\text{radian}\) | 2. | \(\dfrac{\pi}{2}~\text{radian}\) |
| 3. | \({\pi}~\text{radian}\) | 4. | \(\dfrac{\pi}{8}~\text{radian}\) |
On a frictionless surface, a block of mass \(M\) moving at speed \(v\) collides elastically with another block of the same mass \(M\) which is initially at rest. After the collision, the first block moves at an angle \(\theta\) to its initial direction and has a speed \(\frac{v}{3}\). The second block’s speed after the collision will be:
| 1. | \(\frac{2\sqrt{2}}{3}v\) | 2. | \(\frac{3}{4}v\) |
| 3. | \(\frac{3}{\sqrt{2}}v\) | 4. | \(\frac{\sqrt{3}}{2}v\) |
A potentiometer wire of length \(L\) and a resistance \(r\) are connected in series with a battery of EMF \(E_{0 }\) and resistance \(r_{1}\). An unknown EMF is balanced at a length l of the potentiometer wire. The EMF \(E\) will be given by:
1. \(\frac{L E_{0} r}{l r_{1}}\)
2. \(\frac{E_{0} r}{\left(\right. r + r_{1} \left.\right)} \cdot \frac{l}{L}\)
3. \(\frac{E_{0} l}{L}\)
4. \(\frac{L E_{0} r}{\left(\right. r + r_{1} \left.\right) l}\)
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