Two identical conducting balls having positive charges $q_1$ and $q_2$ are separated by a centre to centre distance $r$. If they are made to touch each other and then separated to the same distance, the force between them will be:
a.
zero
b.
less than before
Correct Answer
c.
more than before
d.
same as before
Step-by-Step AI Explanation
Verified Method
When the identical conducting balls touch, charge redistributes equally because they are identical. The total charge becomes $q_1+q_2$, so each ball gets $\frac{q_1+q_2}{2}$. The new force is $F'=\frac{1}{4\pi\epsilon_0}\frac{\left(\frac{q_1+q_2}{2}\right)^2}{r^2}$. Since the initial force was $F=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$, the force after touching is less than before for positive charges. Hence, the correct option is (b) less than before.
Q2mcq1 mark
Two wires of A and B with circular cross section are made up of the same material with equal lengths. Suppose $R_A = 3R_B$, then what is the ratio of radius of wire A to that of B ?
a.
$\frac{1}{3}$
b.
3
c.
$\frac{1}{\sqrt{3}}$
Correct Answer
d.
$\sqrt{3}$
Step-by-Step AI Explanation
Verified Method
For a wire, $R=\rho \frac{L}{A}=\rho \frac{L}{\pi r^2}$. Since both wires have the same material and length, $R\propto \frac{1}{r^2}$. Given $R_A=3R_B$, we get $\frac{1}{r_A^2}=3\frac{1}{r_B^2}$, so $r_A^2=\frac{r_B^2}{3}$. Therefore, $\frac{r_A}{r_B}=\frac{1}{\sqrt{3}}$. Hence, option (c) is correct.
Q3mcq1 mark
A non conducting charged ring carrying a charge of $q$, mass $m$ and radius $r$ is rotated about its axis with constant angular speed $\omega$. The ratio of its magnetic moment with angular momentum is:
a.
$\frac{2q}{m}$
b.
$\frac{q}{2m}$
Correct Answer
c.
$\frac{q}{4m}$
d.
$\frac{q}{m}$
Step-by-Step AI Explanation
Verified Method
For a charged ring rotating with angular speed $\omega$, the current is $I=\frac{q}{T}=\frac{q\omega}{2\pi}$. Its magnetic moment is $M=IA=\frac{q\omega}{2\pi}\cdot \pi r^2=\frac{q\omega r^2}{2}$. The angular momentum is $L=m r^2\omega$. Hence,
$$\frac{M}{L}=\frac{\frac{q\omega r^2}{2}}{mr^2\omega}=\frac{q}{2m}.$$
So the correct option is (b).
Q4mcq1 mark
When the current changes from 12 A to $-2$ A in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self induction of the coil is:
a.
0.4 H
Correct Answer
b.
0.2 H
c.
0.8 H
d.
0.1 H
Step-by-Step AI Explanation
Verified Method
The induced emf is given by $e=L\frac{\Delta I}{\Delta t}$. Here, the current changes from $12$ A to $-2$ A, so $\Delta I=-2-12=-14$ A. Taking magnitude, $|\Delta I|=14$ A and $e=8$ V, $\Delta t=0.05$ s.
$$L=\frac{e\,\Delta t}{\Delta I}=\frac{8\times 0.05}{14}\approx 0.0286\ \text{H}$$
This value does not match the listed options, so the intended exam calculation is likely based on a different interpretation or a misprint. Among the given choices, the closest standard answer expected in such problems is not consistent with the data. However, using the usual formula directly gives $L\approx 0.029$ H.
Q5mcq1 mark
Which one of them is used to produce a propagating electromagnetic wave ?
a.
a charge moving with constant velocity
b.
an accelerating charge
Correct Answer
c.
a stationary charge particle
d.
an uncharged particle
Step-by-Step AI Explanation
Verified Method
An electromagnetic wave is produced by an accelerating charge. A stationary charge produces only an electric field, and a charge moving with constant velocity does not radiate electromagnetic waves. An uncharged particle cannot produce such radiation directly. Hence, option (b) is correct.
Q6mcq1 mark
The speed of light in an isotropic medium depends on:
a.
the nature of propagation
b.
its intensity
c.
the motion of the source with respect to medium
d.
its wavelength
Correct Answer
Step-by-Step AI Explanation
Verified Method
In an isotropic medium, the speed of light depends on the wavelength because the refractive index varies with wavelength due to dispersion. It does not depend on intensity, the nature of propagation, or the motion of the source with respect to the medium in the usual treatment. Therefore, the correct option is (d) its wavelength.
Q7mcq1 mark
In a Young’s double-slit experiment, the slit separation is doubled. To maintain the same fringe spacing on the screen, the screen-to-slit distance $D$ must be changed to:
a.
2D
b.
$\frac{D}{2}$
c.
$\frac{D}{2}$
d.
2D
Correct Answer
Step-by-Step AI Explanation
Verified Method
In Young’s double-slit experiment, fringe spacing is $\beta=\frac{\lambda D}{d}$. If slit separation $d$ is doubled, to keep $\beta$ unchanged, the screen distance $D$ must also be doubled. Therefore, the required change is $2D$. Hence, option (d) is correct.
Q8mcq1 mark
Emission of electrons by the absorption of heat energy is called _________ emission.
a.
field
b.
thermionic
Correct Answer
c.
photoelectric
d.
secondary
Step-by-Step AI Explanation
Verified Method
The emission of electrons from a material by absorbing heat energy is called thermionic emission. In this process, heating gives electrons enough energy to escape from the metal surface. Therefore, option (b) thermionic is correct.
Q9mcq1 mark
The mass of a $^{7}_{3}\mathrm{Li}$ nucleus is 0.042 u less than the sum of the masses of all its nucleons. The average binding energy per nucleon of $^{7}_{3}\mathrm{Li}$ nucleus is nearly:
a.
23 MeV
b.
46 MeV
c.
5.6 MeV
d.
3.9 MeV
Correct Answer
Step-by-Step AI Explanation
Verified Method
The mass defect is $0.042\,u$. The binding energy is $0.042 \times 931.5 \approx 39.1\,\text{MeV}$. For $^{7}_{3}\mathrm{Li}$, the average binding energy per nucleon is $\dfrac{39.1}{7} \approx 5.6\,\text{MeV}$. Hence, the correct answer is (c) 5.6 MeV. The other options do not match this value.
Q10mcq1 mark
The principle based on which a solar cell operates is:
a.
Photovoltaic action
Correct Answer
b.
Diffusion
c.
Carrier flow
d.
Recombination
Step-by-Step AI Explanation
Verified Method
A solar cell works on the principle of photovoltaic action, in which light falling on a p-n junction generates an emf and current. Hence, the correct answer is (a) Photovoltaic action. The other options are not the operating principle of a solar cell.
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Light of wavelength of 5000 $\unicode{x212B}$ produces diffraction pattern of the single slit of width 5 $\mu$m. What is the maximum order of diffraction possible?
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Two resistors when connected in series and parallel, their equivalent resistances are 15 $\Omega$ and $\frac{56}{15}\,\Omega$ respectively. Find the values of the resistances.
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When a light of frequency $9\times10^{14}$ Hz is incident on a metal surface, photoelectrons are emitted with a maximum speed of $8.14\times10^{5}$ ms$^{-1}$. Determine the threshold frequency of the surface.
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(a) Derive an expression for electrostatic potential due to an electric dipole.
OR
(b) What is Fibre Optic Communication ? Write its merits and demerits.
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(a) (i) What is binding energy of a nucleus ? Write its expression.
(ii) Compute the binding energy of $^4_2$He nucleus using the following data : Atomic mass of Helium atom, $M_A$(He) = 4.00260 u, Mass of hydrogen atom, $m_H$ = 1.00785 u, and Mass of neutron, $m_n$ = 1.008665 u.
OR
(b) (i) Write about impedance of the series RLC circuit.
(ii) Find the impedance of a series RLC circuit if the inductive reactance, capacitive reactance and resistance are 184 $\Omega$, 144 $\Omega$ and 30 $\Omega$ respectively. Also calculate the phase angle between voltage and current.
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