NEB Grade XI Physics Model Question Set 5 — Answer Key, Important Questions & Free PDF

Model Question Set 5 brings back some familiar topics from Sets 2-4 (lens maker’s formula, Gauss’s theorem, drift velocity, capacitor combinations) but pairs them with genuinely new mechanics problems — conical pendulums, friction-based block-and-trolley systems, and projectile motion across a river. This set has the most “figure-dependent” questions of the series so far, with three separate diagrams that directly affect the numericals. Below: the answer key, what’s new here, important questions, and the full downloadable paper.

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View the Full Question Paper

Get the complete Model Question Set 5 (Grade XI Physics) as a PDF — includes all diagrams, graphs, and figures referenced in the questions below, including the trolley-pulley system, the box-on-incline diagram, and the specific heat capacity graph.

MCQ Answer Key — Grade XI Physics Model Set 5

All 11 MCQs from Group A, 1 mark each ([latex]11 \times 1 = 11[/latex] marks). Note that Q3 depends on a figure (motion graphs a-d) — see the FAQ for how to identify the correct graph type.

Quick working for tricky ones: Q4 — [latex]g_h = \frac{g}{(1+h/R)^2}[/latex]. Setting [latex]g_h = g/2[/latex] gives latex^2 = 2[/latex], so [latex]1+h/R = \sqrt{2} \approx 1.414[/latex], giving [latex]h = 0.414R[/latex]. Q10 — by Newton’s third law, the force on each charge due to the other is equal and opposite in magnitude regardless of the charge values, so the ratio is always 1:1. Q11 — a neutron is made of one up quark and two down quarks (udd), giving total charge [latex]\frac{2}{3} – \frac{1}{3} – \frac{1}{3} = 0[/latex], consistent with the neutron’s neutral charge.

What’s New in This Set

Compared to Sets 2-4, here’s what Set 5 introduces or emphasizes differently:

• Friction-based dynamics with a figure (Q12): a block-and-trolley system connected by a pulley, requiring free body diagrams and rolling friction — this exact “two-mass-pulley” setup hasn’t appeared in Sets 2-4.
• Conical pendulum (Q12, OR): time period derivation for a bob rotating in a horizontal circle at an angle to the vertical — a genuinely new topic.
• Plane charged conductor (Q17b): Gauss’s theorem applied to a different geometry (infinite plane sheet) rather than the linear charge density seen in Set 4.
• Capacitor network with mixed series-parallel (Q18a): three capacitors in a parallel+series combination — more complex than the simple pairs in earlier sets.
• Projectile motion across a moving river (Q21c): a relative-velocity problem combining river current and swimmer’s velocity — first appearance of 2D relative motion.
• Block on incline with applied force at an angle (Q20c): combines friction, normal force, and force resolution — a classic but previously untested combination.
• Nuclear fission mass consumption rate (Q22c): given energy per fission and reactor power, find mass of U-235 consumed per day — pairs well with Set 4’s fission power question but asks for the reverse quantity.

Important Questions for Your Final Exam

These topics from Set 5 round out areas of the syllabus that Sets 2-4 didn’t fully cover — particularly in mechanics and electrostatics.

• Average speed for equal distances at different speeds (harmonic mean, not arithmetic mean!)
• Height above Earth’s surface where [latex]g[/latex] reduces to a fraction of its surface value
• Critical angle and total internal reflection between two media
• Achromatism condition: [latex]F_R + F_V = 0[/latex]
• Prism refraction — angle of refraction at each face, angle of minimum deviation
• Plano-convex lens focal length using lens maker’s formula
• Free body diagrams for connected systems (block + trolley + pulley) with rolling friction
• Conical pendulum — time period derivation
• Thermal conductivity and rate of ice melting through a lagged bar
• Specific heat capacity from an energy-vs-temperature graph
• Pressure of an ideal gas — derivation and density from rms speed
• Lens maker’s formula — derivation and application
• Refractive index of a prism in terms of refracting angle and angle of minimum deviation
• Gauss’s law — statement and application to a plane charged conductor
• Capacitor combinations — series, parallel, and mixed networks
• Drift velocity and current density relation
• Kirchhoff’s laws for circuit analysis
• Energy density in a stretched wire
• Block on a rough incline with an applied force at an angle — friction and equilibrium
• Projectile motion — maximum height, time of flight, horizontal range
• Relative velocity — swimmer crossing a river with current
• Orbital speed and radial (centripetal) acceleration of a satellite
• Escape velocity as [latex]\sqrt{2}[/latex] times orbital velocity — derivation
• Effect on [latex]g[/latex] if Earth stopped rotating
• Binding energy per nucleon vs. mass number — nuclear stability
• Nuclear density and why it’s nearly constant across nuclei
• Fission: mass of fuel consumed per day for a given reactor power

Frequently Asked Questions

Why is the average speed in Q2 18 km/h and not the simple average of 30 km/h?

When equal distances (not equal times) are covered at different speeds, you cannot simply average the speeds — you must use total distance divided by total time. Let total distance [latex]= 3d[/latex] (so each segment is [latex]d[/latex]). Time for each segment: [latex]t_1 = \frac{d}{10}[/latex], [latex]t_2 = \frac{d}{20}[/latex], [latex]t_3 = \frac{d}{60}[/latex]. Total time [latex]= d\left(\frac{1}{10}+\frac{1}{20}+\frac{1}{60}\right) = d\left(\frac{6+3+1}{60}\right) = \frac{10d}{60} = \frac{d}{6}[/latex]. Average speed [latex]= \frac{3d}{d/6} = 18[/latex] km/h. This harmonic-mean approach is essential whenever distances (not times) are equal.

For Q3, how do you identify the correct motion graph?

“Speed that increases uniformly with time” means [latex]v \propto t[/latex], which means constant acceleration ([latex]a = \frac{dv}{dt} = \text{constant}[/latex]). Looking at the four graph types: a graph of acceleration vs time that is a straight horizontal line would represent constant acceleration directly — but if velocity increases uniformly (linearly) with time, acceleration itself is constant (a horizontal line on an a-t graph), OR if the graph shown is acceleration vs time with a rising straight line, that would represent acceleration that itself increases uniformly (i.e., velocity increasing non-uniformly, following a parabolic curve). Given the typical answer for this classic question is graph (b) — a straight line with positive slope on an acceleration-time axes — this usually corresponds to a scenario where the question intends “uniformly increasing acceleration” rather than uniformly increasing velocity. We recommend checking your specific textbook’s figure labels carefully, since (a) a horizontal a-t line (constant acceleration → uniformly increasing velocity) is the more standard physics answer for “speed increases uniformly with time.”

How do you derive [latex]h = 0.414R[/latex] for Q4?

At height [latex]h[/latex] above Earth’s surface, [latex]g_h = \frac{GM}{(R+h)^2} = \frac{g}{(1+h/R)^2}[/latex] where [latex]g = \frac{GM}{R^2}[/latex] is the surface value. Setting [latex]g_h = \frac{g}{2}[/latex]: [latex]\frac{1}{(1+h/R)^2} = \frac{1}{2}[/latex], so latex^2 = 2[/latex], giving [latex]1 + \frac{h}{R} = \sqrt{2} \approx 1.414[/latex]. Therefore [latex]h = 0.414R[/latex].

How do you find the angle of incidence at the 2nd face of the prism in Q8?

For a prism with refracting angle [latex]A[/latex], the relation between the angles inside the prism is [latex]r_1 + r_2 = A[/latex], where [latex]r_1[/latex] is the angle of refraction at the first face and [latex]r_2[/latex] is the angle of incidence at the second face (measured from the normal). Given [latex]A = 60°[/latex] and [latex]r_1 = 25°[/latex]: [latex]r_2 = A – r_1 = 60° – 25° = 35°[/latex]. This is the angle of incidence at the second face — answer d) 35°. Note: the refractive index (μ=1.5) is extra information for this particular sub-question; it would be needed if you were asked for the angle of emergence at the second face using Snell’s law.

How do you find the focal length of the plano-convex lens in Q9?

Using the lens maker’s formula [latex]\frac{1}{f} = (\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)[/latex]. For a plano-convex lens, one surface is flat ([latex]R_2 = \infty[/latex]) and the other is curved ([latex]R_1 = 60[/latex] cm, taking the convention that gives a positive focal length). So [latex]\frac{1}{f} = (1.6-1)\left(\frac{1}{60}-0\right) = 0.6 \times \frac{1}{60} = \frac{1}{100}[/latex]. Therefore [latex]f = 100[/latex] cm.

How do you approach the block-and-trolley problem in Q12?

This is a connected-system problem with two masses (20 kg trolley, 3 kg hanging weight) linked by a string over a pulley, with the trolley experiencing rolling friction. Draw separate free body diagrams: for the hanging mass, [latex]mg – T = ma[/latex]; for the trolley, [latex]T – f_k = Ma[/latex], where [latex]f_k = \mu_k Mg[/latex] is the rolling friction force ([latex]\mu_k = 0.04[/latex]). Adding both equations: [latex]mg – \mu_k Mg = (M+m)a[/latex]. With [latex]m=3[/latex] kg, [latex]M=20[/latex] kg, [latex]g=10[/latex] m/s², [latex]\mu_k=0.04[/latex]: [latex]a = \frac{(3)(10) – 0.04(20)(10)}{23} = \frac{30-8}{23} = \frac{22}{23} \approx 0.96 , m/s^2[/latex]. Note: the 30N force shown in the figure may represent an additional applied force on the hanging mass — incorporate it according to how your figure is drawn.

How do you find the time period of the conical pendulum in Q12 (OR)?

For a conical pendulum with string length [latex]L=0.5[/latex] m making angle [latex]\theta=30°[/latex] with the vertical, the time period is [latex]T = 2\pi\sqrt{\frac{L\cos\theta}{g}}[/latex]. Substituting: [latex]T = 2\pi\sqrt{\frac{0.5 \times \cos 30°}{10}} = 2\pi\sqrt{\frac{0.5 \times 0.866}{10}} = 2\pi\sqrt{0.0433} \approx 2\pi \times 0.208 \approx 1.31[/latex] seconds.

How do you find the density of the gas in Q15(b)?

Pressure relates to rms speed and density via [latex]P = \frac{1}{3}\rho v_{rms}^2[/latex]. Convert pressure: [latex]700[/latex] mm Hg [latex]= 700 \times 133.3 \approx 93310[/latex] Pa (using 1 mm Hg ≈ 133.3 Pa). Then [latex]\rho = \frac{3P}{v_{rms}^2} = \frac{3 \times 93310}{(400)^2} = \frac{279930}{160000} \approx 1.75 , kg/m^3[/latex].

How do you solve the box-on-incline friction problem in Q20(c)?

The box is on the verge of sliding under a force [latex]X[/latex] applied at 50° above the horizontal. Resolve [latex]X[/latex] into horizontal ([latex]X\cos 50°[/latex]) and vertical ([latex]X\sin 50°[/latex]) components. The normal force [latex]N = mg – X\sin 50°[/latex] (the vertical component of X reduces the normal force if pulling upward, or increases it if pushing downward — check the figure’s arrow direction). At the point of sliding, [latex]X\cos 50° = \mu N = \mu(mg – X\sin 50°)[/latex]. Solving: [latex]X\cos 50° + \mu X \sin 50° = \mu mg[/latex], so [latex]X = \frac{\mu mg}{\cos 50° + \mu\sin 50°}[/latex]. With [latex]m=15[/latex] kg, [latex]\mu=0.15[/latex], [latex]g=10[/latex]: [latex]X = \frac{0.15 \times 15 \times 10}{\cos 50° + 0.15\sin 50°} = \frac{22.5}{0.643 + 0.115} = \frac{22.5}{0.758} \approx 29.7[/latex] N.

How do you solve the river-crossing problem in Q21(c)?

The swimmer’s velocity relative to water is 4 km/h, and the river flows at 3 km/h. To find the direction needed and total distance: if the swimmer aims to minimize drift or reach a specific point, set up the velocity components. For 15 minutes ([latex]t = 0.25[/latex] h), if swimming straight across (perpendicular to the bank) at 4 km/h, the swimmer covers [latex]4 \times 0.25 = 1[/latex] km across (exactly the river width) while drifting downstream by [latex]3 \times 0.25 = 0.75[/latex] km. Total distance covered (resultant displacement) [latex]= \sqrt{1^2+0.75^2} = \sqrt{1+0.5625} = \sqrt{1.5625} = 1.25[/latex] km. The direction to “strike out” would be perpendicular to the bank (straight across) if the goal is to cross in minimum time, with the understanding that the swimmer lands 0.75 km downstream from the starting point’s perpendicular projection.

How do you find the radial acceleration of the satellite in Q21 (OR, a)?

Radial (centripetal) acceleration [latex]a = \frac{v^2}{r}[/latex], where [latex]r[/latex] is the orbital radius. First find [latex]r[/latex] using [latex]v = \sqrt{\frac{GM}{r}}[/latex], so [latex]r = \frac{GM}{v^2}[/latex]. With [latex]GM = 6.67\times 10^{-11} \times 6\times 10^{24} \approx 4\times 10^{14}[/latex] and [latex]v=6200[/latex] m/s: [latex]r = \frac{4\times 10^{14}}{(6200)^2} = \frac{4\times 10^{14}}{3.844\times 10^7} \approx 1.04\times 10^7[/latex] m. Then [latex]a = \frac{v^2}{r} = \frac{(6200)^2}{1.04\times 10^7} = \frac{3.844\times 10^7}{1.04\times 10^7} \approx 3.7 , m/s^2[/latex].

How do you find the mass of U-235 consumed per day in Q22(c)?

Power [latex]=1[/latex] MW [latex]=10^6[/latex] W. Energy needed per day [latex]= 10^6 \times 86400 = 8.64\times 10^{10}[/latex] J. Each fission releases [latex]200[/latex] MeV [latex]= 200\times 1.6\times 10^{-13} = 3.2\times 10^{-11}[/latex] J. Number of fissions per day [latex]= \frac{8.64\times 10^{10}}{3.2\times 10^{-11}} \approx 2.7\times 10^{21}[/latex]. Number of moles [latex]= \frac{2.7\times 10^{21}}{6\times 10^{23}} \approx 4.5\times 10^{-3}[/latex] mol. Mass [latex]= 4.5\times 10^{-3} \times 235 \approx 1.06[/latex] g per day — a striking illustration of how energy-dense nuclear fission is compared to chemical fuels.

How to Use This Set Effectively

Several Group B and C questions here (Q12, Q18a, Q19b, Q20c) depend heavily on figures that you can’t fully reconstruct from text alone — download the PDF above and study the diagrams directly before attempting the numericals. Pay particular attention to force directions, angles, and circuit connections, since a misread diagram is the most common source of errors in these problems even when the formula knowledge is solid.

This set’s mechanics section (Q12, Q20, Q21) is more figure-heavy and conceptually layered than Sets 2-4 — if you found those sets manageable but this one’s mechanics questions confusing, the gap is likely in translating diagrams into free body diagrams and equations, not in the underlying formulas. Practice drawing FBDs for every mechanics problem you attempt, even simple ones, to build this skill.

As with the previous sets, run this as a full 3-hour timed mock exam. Given the higher number of figure-based questions, budget a few extra minutes at the start to study all diagrams before writing anything.