Question 1
According to NCERT, when an electromagnetic wave strikes a surface and is completely absorbed, the momentum delivered to the surface is $p$. If the same wave is completely reflected by a perfectly reflecting surface, what is the momentum delivered to the surface?
✅ Correct Answer: $2p$
Explanation: For a perfectly absorbing surface, the momentum transferred is $p = U/c$. For a perfectly reflecting surface, the wave bounces back with the same speed but opposite direction. The change in momentum of the wave is $p_f - p_i = -p - p = -2p$. Thus, the magnitude of the momentum transferred to the surface is $2p$.
Question 2
As per NCERT, the angle of dip at a place on Earth where the horizontal component of Earth's magnetic field equals the vertical component is:
✅ Correct Answer: $45^\circ$
Explanation: The angle of dip ($\delta$) is given by $\tan(\delta) = B_V / B_H$. If the vertical component ($B_V$) equals the horizontal component ($B_H$), then $\tan(\delta) = 1$. This implies $\delta = 45^\circ$.
Question 3
A point charge $+q$ is moved along a circular path of radius $r$ around another stationary point charge $+Q$ placed at the center. The work done by the electrostatic force in one complete revolution is:
✅ Correct Answer: Zero
Explanation: A circular path around a central charge is an equipotential surface (potential $V$ is constant at distance $r$). The work done in moving a charge along an equipotential surface is always zero because $W = q \Delta V$, and $\Delta V = 0$. Alternatively, force is always perpendicular to displacement.
Question 4
If a physical quantity $Z = \frac{a^2 b^{1/2}}{c^3}$, and the percentage errors in the measurement of $a$, $b$, and $c$ are 1%, 2%, and 3% respectively, what is the maximum percentage error in $Z$?
✅ Correct Answer: $12\%$
Explanation: Using the error formula: $\frac{\Delta Z}{Z} \times 100 = \left(2\frac{\Delta a}{a} + \frac{1}{2}\frac{\Delta b}{b} + 3\frac{\Delta c}{c}\right) \times 100$. Error $= 2(1\%) + \frac{1}{2}(2\%) + 3(3\%) = 2\% + 1\% + 9\% = 12\%$.
Question 5
Consider the following statements about a p-n junction diode:
Statement I: In forward bias, the width of the depletion region decreases.
Statement II: The potential barrier of a silicon p-n junction diode at room temperature is approximately 0.3 V.
✅ Correct Answer: Statement I is correct but Statement II is incorrect.
Explanation: Statement I is correct; forward biasing opposes the built-in potential, narrowing the depletion region. Statement II is incorrect; the potential barrier for Silicon is approximately 0.7 V, while for Germanium it is about 0.3 V.
Question 6
According to NCERT, the core of a transformer is laminated to reduce energy losses due to:
✅ Correct Answer: Eddy currents
Explanation: Laminating the iron core breaks the path for circulating currents (eddy currents) induced by the changing magnetic flux. This greatly increases the electrical resistance of the core, minimizing heat loss due to eddy currents.
Question 7
In the Davisson-Germer experiment highlighted in NCERT, the maximum intensity of the scattered electron beam was observed at:
✅ Correct Answer: Accelerating voltage of $54\text{ V}$ and scattering angle of $50^\circ$
Explanation: The Davisson-Germer experiment experimentally verified the wave nature of electrons. The pronounced diffraction peak (maximum intensity) was historically observed at an accelerating voltage $V = 54\text{ V}$ and a scattering angle $\theta = 50^\circ$.
Question 8
Which of the following is NOT a property of the strong nuclear force?
✅ Correct Answer: It obeys the inverse-square law.
Explanation: Unlike gravitational and electrostatic forces, the strong nuclear force does not obey the inverse-square law ($F \propto 1/r^2$). It is a short-range force that drops rapidly to zero beyond 2-3 fm. It is independent of charge.
Question 9
The dynamic lift experienced by an airplane wing is primarily explained by:
✅ Correct Answer: Bernoulli's Principle
Explanation: The shape of an airplane wing (aerofoil) causes air to travel faster over the top surface than the bottom. According to Bernoulli's principle ($P + \frac{1}{2}\rho v^2 = \text{constant}$), higher speed on top results in lower pressure, creating an upward dynamic lift.
Question 10
Assertion: A diamond sparkles brilliantly more than a similar-cut piece of glass.
Reason: The refractive index of diamond is very high, making its critical angle for total internal reflection very small.
✅ Correct Answer: Both Assertion and Reason are correct and Reason is the correct explanation.
Explanation: Diamond has a high refractive index ($\mu \approx 2.42$), which gives it a very small critical angle ($\theta_c = \sin^{-1}(1/\mu) \approx 24.4^\circ$). Because of this small critical angle, light entering the diamond undergoes multiple total internal reflections before exiting, causing the brilliant sparkle.
Question 11
Assertion: A geostationary satellite must be parked in an orbit directly above the Earth's equator.
Reason: To appear stationary, its orbital plane must be concentric and coplanar with the Earth's equatorial plane, and its time period must exactly match Earth's rotational period.
✅ Correct Answer: Both Assertion and Reason are correct and Reason is the correct explanation.
Explanation: A geostationary satellite revolves around the Earth with a time period of 24 hours. For it to remain fixed relative to a point on the ground, its orbit must lie in the equatorial plane. If it were inclined, it would appear to drift north and south over the course of the day.
Question 12
Consider the following two statements regarding sound waves:
Statement I: Beat frequency is heard when two sound waves of exactly the same frequency and amplitude interfere.
Statement II: The Doppler effect in sound is asymmetric, meaning the apparent frequency depends on whether the source is moving towards the observer or the observer is moving towards the source with the same speed.
✅ Correct Answer: Statement I is incorrect but Statement II is correct.
Explanation: Statement I is incorrect; beats are produced by the superposition of two waves with slightly different frequencies. Statement II is correct; Doppler effect in sound is asymmetric because sound requires a medium.
Question 13
A solid sphere rolls without slipping on a horizontal surface. The ratio of its rotational kinetic energy to its total kinetic energy is:
✅ Correct Answer: $2/7$
Explanation: Rotational $KE = \frac{1}{2}I\omega^2 = \frac{1}{2}(\frac{2}{5}MR^2)(v/R)^2 = \frac{1}{5}Mv^2$. Translational $KE = \frac{1}{2}Mv^2$. Total $KE = \frac{1}{5}Mv^2 + \frac{1}{2}Mv^2 = \frac{7}{10}Mv^2$. Ratio $= \frac{1/5}{7/10} = \frac{2}{7}$.
Question 14
In a macroscopic conductor, if the area of cross-section is doubled while the current flowing through it is kept constant, what happens to the drift velocity of the free electrons?
✅ Correct Answer: It becomes half.
Explanation: Current is related to drift velocity by $I = neAv_d$. Rearranging gives $v_d = I/(neA)$. Since current ($I$), charge ($e$), and number density ($n$) remain constant, $v_d \propto 1/A$. If the area ($A$) is doubled, the drift velocity ($v_d$) is halved.
Question 15
In an experiment on the photoelectric effect, a graph is plotted between the stopping potential ($V_0$) on the y-axis and the frequency of incident light ($\nu$) on the x-axis. The slope of this straight line gives:
✅ Correct Answer: Ratio of Planck's constant to electron charge ($h/e$)
Explanation: According to Einstein's photoelectric equation: $eV_0 = h\nu - \Phi_0$. Rearranging for $V_0$: $V_0 = (h/e)\nu - (\Phi_0/e)$. Comparing this with the equation of a straight line $y=mx+c$, the slope $m$ is equal to $h/e$.
Question 16
A boatman can row his boat with a speed of $5\text{ km/h}$ in still water. He wants to cross a river of width $1\text{ km}$ flowing at a speed of $3\text{ km/h}$ along the shortest possible path. What is the time taken by him to cross the river?
✅ Correct Answer: $1/4\text{ hour}$
Explanation: For the shortest path (straight across, perpendicular to flow), the boatman must row at an angle upstream. His net velocity $v_{net}$ perpendicular to the river flow is given by Pythagoras theorem: $v_{net} = \sqrt{v_{boat}^2 - v_{river}^2} = \sqrt{5^2 - 3^2} = \sqrt{16} = 4\text{ km/h}$. Time taken $t = \text{Distance}/v_{net} = 1\text{ km} / 4\text{ km/h} = 1/4\text{ hour}$ (or 15 mins).
Question 17
A parallel plate capacitor with air has a capacitance $C$. A dielectric slab of dielectric constant $K$ is introduced, filling only the lower half of the space between the plates (parallel to the plates). The new capacitance will be:
✅ Correct Answer: $2CK/(K+1)$
Explanation: Inserting the slab parallel to the plates divides the capacitor into two capacitors in series, each with distance $d/2$. Capacitance of upper air half: $C_1 = \frac{\varepsilon_0 A}{d/2} = 2C$. Capacitance of lower dielectric half: $C_2 = \frac{K \varepsilon_0 A}{d/2} = 2KC$. Equivalent capacitance in series: $C_{eq} = \frac{C_1 C_2}{C_1+C_2} = \frac{(2C)(2KC)}{2C + 2KC} = \frac{4KC^2}{2C(K+1)} = \frac{2CK}{K+1}$.
Question 18
Two springs of spring constants $k_1$ and $k_2$ are connected in series. A block of mass $m$ is suspended from the combination. If the block is displaced vertically, the time period of its simple harmonic motion is:
✅ Correct Answer: $2\pi \sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$
Explanation: For springs connected in series, the equivalent spring constant $k_{eq}$ is given by $\frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2} \implies k_{eq} = \frac{k_1 k_2}{k_1+k_2}$. The time period of SHM is $T = 2\pi\sqrt{m/k_{eq}}$. Substituting $k_{eq}$ gives $T = 2\pi\sqrt{\frac{m(k_1+k_2)}{k_1 k_2}}$.
Question 19
An ideal Carnot refrigerator operates between temperatures of $27^\circ\text{C}$ and $-3^\circ\text{C}$. What is its coefficient of performance (COP)?
✅ Correct Answer: $9$
Explanation: First, convert temperatures to Kelvin. Cold reservoir $T_2 = -3^\circ\text{C} = 270\text{ K}$. Hot reservoir $T_1 = 27^\circ\text{C} = 300\text{ K}$. For a refrigerator, $\text{COP} (\beta) = \frac{T_2}{T_1-T_2}$. $\beta = \frac{270}{300-270} = \frac{270}{30} = 9$.
Question 20
TRAP QUESTION: A particle is projected from the ground with an initial velocity $u$ at an angle $\theta$ to the horizontal. Ignoring air resistance, what is the magnitude of the change in its momentum between its point of projection and its point of impact on the ground?
✅ Correct Answer: $2mu \sin\theta$
Explanation: Let mass be $m$. Initial velocity vector: $u_i = u\cos\theta \hat{i} + u\sin\theta \hat{j}$. Final velocity vector at impact (horizontal velocity is constant, vertical is reversed): $u_f = u\cos\theta \hat{i} - u\sin\theta \hat{j}$. Change in velocity $\Delta v = u_f - u_i = -2u\sin\theta \hat{j}$. Magnitude of change in momentum $= m|\Delta v| = 2mu\sin\theta$.
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