A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
| 1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
| 4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
Pick the wrong statement in the context with a rainbow.
| 1. | Rainbow is a combined effect of dispersion, refraction, and reflection of sunlight. |
| 2. | When the light rays undergo two internal reflections in a water drop, a secondary rainbow is formed. |
| 3. | The order of colors is reversed in the secondary rainbow. |
| 4. | An observer can see a rainbow when his front is towards the sun. |
| 1. | \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\) | 2. | \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\) |
| 3. | \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\) | 4. | \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\) |
Which of the following acts as a circuit protection device?
| 1. | Fuse | 2. | Conductor |
| 3. | Inductor | 4. | Switch |
| 1. | \(\frac{4F}{3}\) | 2. | \(F\) |
| 3. | \(\frac{9F}{16}\) | 4. | \(\frac{16F}{9}\) |
Which colour of the light has the longest wavelength?
1. violet
2. red
3. blue
4. green
The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
| 1. | \(2\) protons only. |
| 2. | \(2\) protons and \(2\) neutrons only. |
| 3. | \(2\) electrons, \(2\) protons, and \(2\) neutrons. |
| 4. | \(2\) electrons and \(4\) protons only. |
A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6~\text{N-m}\)
2. \(2\times 10^{-6}~\text{N-m}\)
3. \(2\times 10^{-3}~\text{N-m}\)
4. \(12\times 10^{-4}~\text{N-m}\)
In a double-slit experiment, when the light of wavelength \(400~\text{nm}\) was used, the angular width of the first minima formed on a screen placed \(1~\text{m}\) away, was found to be \(0.2^{\circ}.\) What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? \(\left(\mu_{\text{water}} = \dfrac{4}{3}\right)\)
1. \(0.1^{\circ}\)
2. \(0.266^{\circ}\)
3. \(0.15^{\circ}\)
4. \(0.05^{\circ}\)