A hollow metal sphere of radius \(R\) is given \(+Q\) charges to its outer surface. The electric potential at a distance \(\dfrac{R}{3}\) from the centre of the sphere will be:
1.
\(\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{9R}\)
2.
\(\dfrac{3}{4\pi \varepsilon_0}\dfrac{Q}{R}\)
3.
\(\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{3R}\)
4.
\(\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{R}\)
| 1. | \(\left[M^2LT^{-2}A^{-2}\right]\) | 2. | \(\left[MLT^{-2}A^{2}\right]\) |
| 3. | \(\left[M^{2}L^{2}T^{-2}A^{2}\right]\) | 4. | \(\left[ML^{2}T^{-2}A^{-2}\right]\) |
The plot of current \(I~\text{(A)}\) flowing through a metallic conductor versus the applied voltage \(V~\text{(volt)}\) across the ends of a conductor is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A network of resistors is connected across a \(10~\text{V}\) battery with an internal resistance of \(1~\Omega\) as shown in the circuit diagram. The equivalent resistance of the circuit is:
| 1. | \(\dfrac{17}{3}~\Omega\) | 2. | \(\dfrac{14}{3}~\Omega\) |
| 3. | \(\dfrac{12}{7}~\Omega\) | 4. | \(\dfrac{14}{7}~\Omega\) |
When a body of mass \(m\) just begins to slide as shown, match List-I with List-II:
| List-I | List-II | ||
| (a) | Normal reaction | (i) | \(P\) |
| (b) | Frictional force \((f_s)\) | (ii) | \(Q\) |
| (c) | Weight \((mg)\) | (iii) | \(R\) |
| (d) | \(mg \mathrm{sin}\theta ~\) | (iv) | \(S\) |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (ii) | (i) | (iii) | (iv) |
| 2. | (iv) | (ii) | (iii) | (i) |
| 3. | (iv) | (iii) | (ii) | (i) |
| 4. | (ii) | (iii) | (iv) | (i) |
| 1. | \(10~\text{J}\) | 2. | \(2.5~\text{J}\) |
| 3. | \(20~\text{J}\) | 4. | \(5~\text{J}\) |
The value of resistance for the colour code of the given resistor is:
1. \((36\pm36)~k\Omega~\)
2. \((470\pm47)~k\Omega~\)
3. \((360\pm36)~k\Omega~\)
4. \((360\pm18)~k\Omega~\)
A concave lens with a focal length of \(-25~\text{cm}\) is sandwiched between two convex lenses, each with a focal length of \(40~\text{cm}.\) The power (in diopters) of the combined lens system would be:
| 1. | \(55\) | 2. | \(9\) |
| 3. | \(1\) | 4. | \(0.01\) |
A beam of light is incident vertically on a glass slab of thickness \(1~\text{cm},\) and refractive index \(1.5.\) A fraction \(A\) is reflected from the front surface while another fraction \(B\) enters the slab and emerges after reflection from the back surface. The time delay between them is:
| 1. | \(10^{-10}~\text{s}\) | 2. | \(5\times 10^{-10}~\text{s}\) |
| 3. | \(10^{-11}~\text{s}\) | 4. | \(5\times 10^{-11}~\text{s}\) |
At some instant, the number of radioactive atoms in a sample is \(N_0\) and after time \(t\), the number decreases to \(N\). It is found that the graphical representation \(\mathrm{ln} N\) versus \(t\) along the \(y\) and \(x\) axis respectively is a straight line. Then the slope of this line is:
1. \(\lambda\)
2. \(-\lambda\)
3. \(\lambda^{-1}\)
4. \(-\lambda^{-1}\)
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