An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 J/s, then the rate at which internal energy increases will be :
1. 125 W
2. 75 W
3. 100 W
4. 25 W
1. 125 W
2. 75 W
3. 100 W
4. 25 W
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A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of \(3.14 \times 10^{-3}\) T at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively :
(Take \(\mu_0 = 4\pi \times 10^{-7}\) T m/A)
1. \(2\text{ A}, 4\text{ A m}^2\)
2. \(2.5\text{ A}, 20\text{ A m}^2\)
3. \(2.5\text{ A}, 2\text{ A m}^2\)
4. \(2\text{ A}, 10\text{ A m}^2\)
(Take \(\mu_0 = 4\pi \times 10^{-7}\) T m/A)
1. \(2\text{ A}, 4\text{ A m}^2\)
2. \(2.5\text{ A}, 20\text{ A m}^2\)
3. \(2.5\text{ A}, 2\text{ A m}^2\)
4. \(2\text{ A}, 10\text{ A m}^2\)
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In Young's double slit experiment, using monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where the path difference is \(\lambda\) is \(K\) units. The intensity of light where the path difference is \(\dfrac{\lambda}{3}\) will be:
1. \(\dfrac{K}{2}\)
2.\(2K\)
3. \(\dfrac K4\)
4. \(K\)
1. \(\dfrac{K}{2}\)
2.\(2K\)
3. \(\dfrac K4\)
4. \(K\)
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The current \(I\) in the circuit shown below is:
(All diodes are ideal and identical.)
1. \(\dfrac{5}{3}~\text{A}\)
2. \(\dfrac{5}{9} ~\text{A}\)
3. \(\dfrac{15}{2} ~\text{A}\)
4. \(\dfrac{1}{3} ~\text{A}\)
(All diodes are ideal and identical.)
1. \(\dfrac{5}{3}~\text{A}\)
2. \(\dfrac{5}{9} ~\text{A}\)
3. \(\dfrac{15}{2} ~\text{A}\)
4. \(\dfrac{1}{3} ~\text{A}\)
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In a concave lens, a ray of light emanating from the object parallel to the principal axis of the lens, after refraction:
| 1. | passes through the second principal focus. |
| 2. | appears to diverge from the first principal focus. |
| 3. | emerges parallel to the principal axis. |
| 4. | passes through 2F, which is the radius of curvature of the lens. |
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A galvanometer of resistance \(100~\Omega\) gives full-scale deflection for a current of \(1\) mA. It is converted into an ammeter of range \(0\text-10\) A. The shunt required is:
1. \(0.10~\Omega\)
2. \(0.001~\Omega\)
3. \(1.0~\Omega\)
4. \(0.01~\Omega\)
1. \(0.10~\Omega\)
2. \(0.001~\Omega\)
3. \(1.0~\Omega\)
4. \(0.01~\Omega\)
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In the first excited state of hydrogen atom, the energy of its electron is \(-3.4 \text{ eV}\). The radial distance of the electron from the hydrogen nucleus in this case is approximately:
(Take \(1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}\), \(e = 1.6 \times 10^{-19} \text{ C}\) and \(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2\))
1. \(2.1 \times 10^{-11} \text{ m}\)
2. \(2.1 \times 10^{-10} \text{ m}\)
3. \(2.1 \times 10^{-9} \text{ m}\)
4. \(2.1 \times 10^{-8} \text{ m}\)
(Take \(1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}\), \(e = 1.6 \times 10^{-19} \text{ C}\) and \(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2\))
1. \(2.1 \times 10^{-11} \text{ m}\)
2. \(2.1 \times 10^{-10} \text{ m}\)
3. \(2.1 \times 10^{-9} \text{ m}\)
4. \(2.1 \times 10^{-8} \text{ m}\)
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The amount of work done to raise a mass 'm' from the surface of the Earth to a height equal to the radius of the Earth 'R', will be:
1. mg R
2. 2 mg R
3. mg \(\frac{R}{4}\)
4. mg \(\frac{R}{2}\)
1. mg R
2. 2 mg R
3. mg \(\frac{R}{4}\)
4. mg \(\frac{R}{2}\)
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An ac circuit contains a resistance of 1 kΩ, a capacitor of 0.1 μF and an inductor of 1 mH connected in series. The resonance frequency of the circuit is approximately :
1. 13.5 kHz
2. 15.9 kHz
3. 10.1 kHz
4. 20.7 kHz
1. 13.5 kHz
2. 15.9 kHz
3. 10.1 kHz
4. 20.7 kHz
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Consider two uncharged capacitors of equal capacitance 200 pF. One of them is charged by a 100 V supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is :
1. 1.0 J
2. 0.5 J
3. 1.0 × 10-6 J
4. 0.5 × 10-6 J
1. 1.0 J
2. 0.5 J
3. 1.0 × 10-6 J
4. 0.5 × 10-6 J
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