The 15 one-mark questions from the Supplementary 2021 12th Standard Physics public exam, in paper order, with the correct option marked and a short explanation.
Q1
Which charge configuration produces a uniform electric field?
- A. Uniformly charged infinite planeCorrect
- B. Point charge
- C. Uniformly charged spherical shell
- D. Uniformly charged infinite line
Explanation. The field of an infinite uniformly charged plane is \(E=\frac{\sigma}{2\varepsilon_0}\), independent of distance, so it is uniform. The fields of a point charge, shell and line all decrease with distance.
Q2
The blueprint for making ultra durable synthetic material is mimicked from:
- A. Parrot fishCorrect
- B. Lotus leaf
- C. Peacock feather
- D. Morpho butterfly
Explanation. The teeth of the parrot fish, made of tightly woven crystal fibres, serve as the biomimetic model for ultra durable synthetic materials. Lotus leaf inspires self-cleaning surfaces, and the Morpho butterfly and peacock feather inspire structural colour.
Q3
In a transformer, the number of turns in the primary and the secondary are 410 and 1230 respectively. If the current in primary is 6 A, then that in the secondary coil is:
- A. 12 A
- B. 2 ACorrect
- C. 1 A
- D. 18 A
Explanation. For an ideal transformer \(\frac{I_s}{I_p}=\frac{N_p}{N_s}\), so \(I_s=6\times\frac{410}{1230}=2\) A.
Q4
Which of the following is false for electromagnetic waves?
- A. longitudinalCorrect
- B. transverse
- C. produced by accelerating charges
- D. non-mechanical waves
Explanation. Electromagnetic waves are transverse (E and B are perpendicular to the direction of propagation), are produced by accelerating charges and need no medium. So "longitudinal" is false.
Q5
If the nuclear radius of \(^{27}\text{Al}\) is 3.6 fermi, the approximate nuclear radius of \(^{64}\text{Cu}\) in fermi is:
- A. 4.8Correct
- B. 2.4
- C. 3.6
- D. 1.2
Explanation. Since \(R\propto A^{1/3}\), \(R_{Cu}=3.6\times\left(\frac{64}{27}\right)^{1/3}=3.6\times\frac{4}{3}=4.8\) fermi.
Q6
The unit of electric flux is:
- A. \(\text{Nm}^{-1}\text{C}^{2}\)
- B. \(\text{Nm}^{-2}\text{C}^{-1}\)
- C. \(\text{Nm}^{2}\text{C}^{-1}\)Correct
- D. \(\text{N}^{2}\text{mC}^{-1}\)
Explanation. Electric flux \(\Phi_E=EA\); E is in \(\text{NC}^{-1}\) and A in \(\text{m}^2\), so the unit is \(\text{Nm}^{2}\text{C}^{-1}\).
Q7
In an oscillating LC circuit, the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is:
- A. \(\frac{Q}{\sqrt{2}}\)Correct
- B. \(\frac{Q}{2}\)
- C. \(Q\)
- D. \(\frac{Q}{\sqrt{3}}\)
Explanation. Total energy \(\frac{Q^2}{2C}\). When shared equally, electric energy \(\frac{q^2}{2C}=\frac{1}{2}\cdot\frac{Q^2}{2C}\), so \(q=\frac{Q}{\sqrt{2}}\).
Q8
The ratio of magnetic length and geometrical length is:
- A. 0.833Correct
- B. 0.633
- C. 0.933
- D. 0.733
Explanation. The magnetic length of a bar magnet is about \(\frac{5}{6}\) of its geometrical length, so the ratio is \(\frac{5}{6}\approx0.833\).
Q9
The Zener diode is primarily used as:
- A. Oscillator
- B. Rectifier
- C. Voltage regulatorCorrect
- D. Amplifier
Explanation. In reverse breakdown a Zener diode keeps the voltage across it nearly constant over a wide range of current, so it is mainly used as a voltage regulator.
Q10
If the Velocity and Wavelength of light in air is \(V_a\) and \(\lambda_a\) and that in water is \(V_w\) and \(\lambda_w\), then the refractive index of water is:
- A. \(\frac{\lambda_w}{\lambda_a}\)
- B. \(\frac{V_w}{V_a}\)
- C. \(\frac{V_a\lambda_a}{V_w\lambda_w}\)
- D. \(\frac{V_a}{V_w}\)Correct
Explanation. Refractive index \(n=\frac{V_a}{V_w}\) (also equal to \(\frac{\lambda_a}{\lambda_w}\), since frequency does not change).
Q11
For a healthy eye, the distance of the near point is ______.
- A. 30 cm
- B. 20 cm
- C. 35 cm
- D. 25 cmCorrect
Explanation. The least distance of distinct vision (near point) of a normal eye is 25 cm.
Q12
The internal resistance of a 2.1 V cell which gives a current of 0.2 A through a resistance of 10 Ω is:
- A. 0.8 Ω
- B. 0.2 Ω
- C. 1.0 Ω
- D. 0.5 ΩCorrect
Explanation. \(I=\frac{\xi}{R+r}\Rightarrow 0.2=\frac{2.1}{10+r}\Rightarrow 10+r=10.5\), so \(r=0.5\ \Omega\).
Q13
A particle having mass m and charge q accelerated through a potential difference V. Find the force experienced when it is kept under perpendicular magnetic field \(\vec{B}\).
- A. \(\sqrt{\frac{2q^3B^2V}{m}}\)Correct
- B. \(\sqrt{\frac{2q^3BV}{m}}\)
- C. \(\sqrt{\frac{2q^3BV}{m^3}}\)
- D. \(\sqrt{\frac{q^3B^2V}{2m}}\)
Explanation. \(\frac{1}{2}mv^2=qV\Rightarrow v=\sqrt{\frac{2qV}{m}}\). Force \(F=qvB=qB\sqrt{\frac{2qV}{m}}=\sqrt{\frac{2q^3B^2V}{m}}\).
Q14
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. \(\sqrt{2}\,D\)
- B. \(2D\)Correct
- C. \(\frac{D}{\sqrt{2}}\)
- D. \(\frac{D}{2}\)
Explanation. Fringe width \(\beta=\frac{\lambda D}{d}\). If d becomes 2d, β stays the same only if D becomes 2D.
Q15
Emission of electrons by the absorption of heat energy is called ______ emission.
- A. ThermionicCorrect
- B. Photoelectric
- C. Secondary
- D. Field
Explanation. When a metal is heated, its free electrons gain enough thermal energy to escape; this is thermionic emission.
