The number of photons per second on an average emitted by a source of monochromatic light of wavelength \(600~\text{nm}\), when it delivers the power of \(3.3\times 10^{-3}\) watt will be:\((h = 6.6\times10^{-34}~\text{J-s})\)
1. \(10^{16}\)
2. \(10^{15}\)
3. \(10^{18}\)
4. \(10^{17}\)
A parallel plate capacitor has a uniform electric field \(\vec{E}\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A\) the energy stored in the capacitor is:
\(\left ( \varepsilon_{0} = \text{permittivity of free space} \right )\)
| 1. | \(\dfrac{1}{2}\varepsilon_0 E^2 Ad\) | 2. | \(\dfrac{E^2 Ad}{\varepsilon_0}\) |
| 3. | \(\dfrac{1}{2}\varepsilon_0 E^2 \) | 4. | \(\varepsilon_0 EAd\) |
\(V=V_0 \sin \omega t\)
The displacement current between the plates of the capacitor would then be given by:
| 1. | \( I_d=\dfrac{V_0}{\omega C} \sin \omega t \) | 2. | \( I_d=V_0 \omega C \sin \omega t \) |
| 3. | \( I_d=V_0 \omega C \cos \omega t \) | 4. | \( I_d=\dfrac{V_0}{\omega C} \cos \omega t\) |
| 1. | \(\sqrt{\dfrac{R_1}{R_2}}\) | 2. | \(\dfrac{R^2_1}{R^2_2}\) |
| 3. | \(\dfrac{R_1}{R_2}\) | 4. | \(\dfrac{R_2}{R_1}\) |
An electromagnetic wave of wavelength \(\lambda\) is incident on a photosensitive surface of negligible work function. If '\(m\)' is the mass of photoelectron emitted from the surface and \(\lambda_d\) is the de-Broglie wavelength, then:
| 1. | \( \lambda=\left(\dfrac{2 {mc}}{{h}}\right) \lambda_{{d}}^2 \) | 2. | \( \lambda=\left(\dfrac{2 {h}}{{mc}}\right) \lambda_{{d}}^2 \) |
| 3. | \( \lambda=\left(\dfrac{2 {m}}{{hc}}\right) \lambda_{{d}}^2\) | 4. | \( \lambda_{{d}}=\left(\dfrac{2 {mc}}{{h}}\right) \lambda^2 \) |
A spring is stretched by \(5~\text{cm}\) by a force \(10~\text{N}\). The time period of the oscillations when a mass of \(2~\text{kg}\) is suspended by it is:
1. \(3.14~\text{s}\)
2. \(0.628~\text{s}\)
3. \(0.0628~\text{s}\)
4. \(6.28~\text{s}\)
An infinitely long straight conductor carries a current of \(5~\text{A}\) as shown. An electron is moving with a speed of \(10^5~\text{m/s}\) parallel to the conductor. The perpendicular distance between the electron and the conductor is \(20~\text{cm}\) at an instant. Calculate the magnitude of the force experienced by the electron at that instant.
1. \(4\pi\times 10^{-20}~\text{N}\)
2. \(8\times 10^{-20}~\text{N}\)
3. \(4\times 10^{-20}~\text{N}\)
4. \(8\pi\times 10^{-20}~\text{N}\)
The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:
1.
2.
3.
4.
Match Column-I and Column-II and choose the correct match from the given choices.
| Column-I | Column-II | ||
| (A) | Root mean square speed of gas molecules | (P) | \(\dfrac13nm\bar v^2\) |
| (B) | The pressure exerted by an ideal gas | (Q) | \( \sqrt{\dfrac{3 R T}{M}} \) |
| (C) | The average kinetic energy of a molecule | (R) | \( \dfrac{5}{2} R T \) |
| (D) | The total internal energy of a mole of a diatomic gas | (S) | \(\dfrac32k_BT\) |
| (A) | (B) | (C) | (D) | |
| 1. | (Q) | (P) | (S) | (R) |
| 2. | (R) | (Q) | (P) | (S) |
| 3. | (R) | (P) | (S) | (Q) |
| 4. | (Q) | (R) | (S) | (P) |
1. \([ML^0T^0]\)
2. \([M^2L^{-2}T^{-1}]\)
3. \([M^2L^{-1}T^{0}]\)
4. \([ML^{-1}T^{-1}]\)
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