NEB Class 11 · Past paper
The complete NEB Class 11 2072 exam paper for Physics, all 12 questions with solved model answers.
Tap a question to open its answer.
Answer, in brief, any six questions: (a) A rod is exactly 1 cm. Readings 1.0, 1.00, 1.000 cm: which is most accurate? (b) A = 4.00 i + 3.00 j, B = 5.00 i - 2.00 j. Find the magnitude of each. (c) At what condition does a body become weightless at the equator? (d) Why is a handle fixed at the free end of a door? (e) What is elastic limit and breaking stress? (f) Why is a suction effect felt when a fast train passes? (g) Why does a cricketer lower his hands while catching a ball?
(a) The reading with the most significant figures (decimal places) is the most precise: 1.000 cm (measured to the nearest thousandth) is the most accurate. (b) Magnitudes of the two vectors: $$ \begin{aligned} \vec A &= \sqrt{4.00^2 + 3....
Answer, in brief, any two questions: (a) Difference between saturated and unsaturated vapour. (b) When a gas expands adiabatically it does work but has no heat input; where does the energy come from? (c) On reducing the volume of a gas at constant temperature, pressure increases. Why?
(a) Saturated vapour is a vapour in equilibrium with its own liquid (maximum vapour density at that temperature, exerting the saturated vapour pressure). Unsaturated vapour is one whose density/pressure is below the saturation value, so ...
Answer, in brief, any one question: (a) Define luminous intensity and its unit. (b) In dispersion by a prism, red appears at the top and violet at the bottom. Why?
(a) Luminous intensity is the luminous flux emitted by a source per unit solid angle in a given direction:
$$I = \frac{\Phi}{\omega}$$
Its SI unit is the candela (cd).
(b) A prism deviates light by an amount that depends on refractive index, which is larger for shorter wavelengths: $\mu_{violet} > \mu_{red}$. So violet is deviated most (bent most toward the base) and red least. With the usual orientation this places red at the top of the spectrum and violet at the bottom.
Answer, in brief, any one question: (a) What is electrostatic shielding? (b) Two charged conductors are touched and separated. What is the charge on them?
(a) Electrostatic shielding is the protection of a region from external electric fields by enclosing it in a conductor (a hollow conductor or cage). Since the field inside a conductor is zero, charges/fields outside cannot penetrate the cavity; this is why sensitive equipment is placed in a metal (Faraday) cage.
(b) On contact the charge redistributes until both reach the same potential. For two identical spheres the total charge shares equally, each getting $\dfrac{Q_1 + Q_2}{2}$. (For unequal conductors it distributes according to their capacitances to keep potentials equal.) If the charges were equal and opposite, they neutralise.
Answer any three questions: (a) State Newton's laws of motion and show they lead to conservation of linear momentum. (b) What is a geostationary satellite? Derive its time period. (c) Define moment of inertia and radius of gyration; derive the KE of rotation. (d) Define surface tension and angle of contact; deduce the rise of liquid in a capillary tube.
(a) Newton's laws: the first law (inertia), the second law ($\vec F = \dfrac{d\vec p}{dt}$), and the third law (action equals reaction). For two colliding bodies with no external force, the third law makes the internal forces equal and o...
Answer any two questions: (a) State and explain Newton's law of cooling; describe a method to measure specific heat capacity of a liquid. (b) Explain thermodynamic process and obtain the work done by a gas during adiabatic expansion. (c) State and explain Stefan's law of black body radiation. Can a perfect black body be realized?
(a) Newton's law of cooling states that, for a small temperature excess, the rate at which a body loses heat is proportional to the difference between its temperature and that of its surroundings:
$$\frac{d\theta}{dt} \propto (\theta - \theta_0)$$
To find the specific heat capacity of a liquid by the cooling-curve method, equal volumes of the test liquid and of water (whose specific heat is known) are allowed to cool in the same calorimeter under identical surroundings through the same range of temperature. Since the rate of heat loss is fixed by the surroundings and is the same at each temperature, the times taken to cool are in the ratio of the heat capacities, and comparing these cooling times gives the liquid's specific heat capacity.
(b) A thermodynamic process is any change that takes a system from one state $(P, V, T)$ to another, such as an isothermal, adiabatic, isobaric or isochoric change. For an adiabatic expansion the gas follows $PV^\gamma = k$, and the work done from $V_1$ to $V_2$ is
$$ \begin{aligned} W &= \int_{V_1}^{V_2} P,dV \ &= \frac{P_1V_1 - P_2V_2}{\gamma - 1} \ &= \frac{nR(T_1 - T_2)}{\gamma - 1} \end{aligned} $$
(c) Stefan's law says that the total energy radiated per unit area per unit time by a black body is proportional to the fourth power of its absolute temperature,
$$E = \sigma T^4$$
where the Stefan constant is $\sigma = 5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$. A perfect black body (one that absorbs every bit of radiation falling on it, $a = 1$) cannot be made exactly, but a small hole in a hollow enclosure with blackened inner walls behaves almost like one: radiation entering the hole is reflected and absorbed again and again inside, so the hole absorbs (and emits) essentially as an ideal black body.
Answer any one question: (a) Discuss refraction through a prism and derive the refractive index in terms of the angle of minimum deviation. (b) With a ray diagram, explain the compound microscope and obtain its magnifying power when the image is at the near point.
(a) For a prism (angle $A$), a ray refracts at both faces; the total deviation is $\delta = (i1 + i2) - A$ with $r1 + r2 = A$. At minimum deviation the ray passes symmetrically: $i1 = i2 = i$ and $r1 = r2 = r$, so $r = A/2$ and
Answer any one question: (a) What is electric flux? State Gauss's law and use it to find the field due to an infinite plane sheet of charge. (b) Obtain relations for equivalent capacitance in series and parallel.
(a) The electric flux through a surface measures how many field lines cross it, defined as
$$\Phi = \oint \vec E\cdot d\vec A$$
Gauss's law states that the total flux out of any closed surface equals the enclosed charge divided by the permittivity of free space:
$$\oint \vec E\cdot d\vec A = \frac{q_{enc}}{\varepsilon_0}$$
To find the field of an infinite plane sheet carrying surface charge density $\sigma$, we take a cylindrical pillbox (each flat face of area $A$) piercing the sheet. By symmetry the field comes straight out of both faces, so the flux is $2EA$ while the charge enclosed is $\sigma A$:
$$2EA = \frac{\sigma A}{\varepsilon_0}$$
Cancelling $A$ gives
$$\boxed{E = \frac{\sigma}{2\varepsilon_0}}$$
which is independent of distance from the sheet.
(b) In a series combination every capacitor carries the same charge $Q$ while the voltages add up:
$$ \begin{aligned} V &= V_1 + V_2 + \dots \ &= \frac{Q}{C_1}+\frac{Q}{C_2}+\dots \end{aligned} $$
Dividing through by $Q$ gives the equivalent series capacitance,
$$\boxed{\frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} + \dots}$$
In a parallel combination every capacitor has the same voltage $V$ while the charges add:
$$Q = C_1V + C_2V + \dots$$
so dividing by $V$ gives
$$\boxed{C_p = C_1 + C_2 + \dots}$$
Answer any three numerical questions: (a) A plane flies 90.0 m/s at 23.0 degrees above horizontal; at 114 m directly above a dog a suitcase drops. How far from the dog will it land? (b) A 20 N rock is thrown up; at 15 m it moves at 25 m/s upward. Find (i) speed leaving the ground and (ii) maximum height. (c) A 0.8 kg stone on a 0.9 m string (breaks at 600 N) whirled in a horizontal circle. Find max speed. (d) Castor oil (viscosity 2.42 Ns/m^2, density 940 kg/m^3): terminal velocity of a 2.00 mm steel ball (steel density 7800 kg/m^3).
(a) The suitcase is released from a plane moving at $90.0\ \text{m/s}$ at $23.0^\circ$ above the horizontal, from $114\ \text{m}$ above the dog, with $g = 9.8\ \text{m/s}^2$. It leaves with the plane's velocity, so its horizontal and vertical components are
$$ \begin{aligned} u_x &= 90\cos23^\circ \ &= 82.85\ \text{m/s} \ u_y &= 90\sin23^\circ \ &= 35.16\ \text{m/s (upward)} \end{aligned} $$
Taking up as positive, the vertical motion from a height of $114\ \text{m}$ gives
$$0 = 114 + 35.16t - 4.9t^2$$
which rearranges to the quadratic
$$4.9t^2 - 35.16t - 114 = 0$$
Solving for the positive root,
$$ \begin{aligned} t &= \frac{35.16 + \sqrt{35.16^2 + 4(4.9)(114)}}{9.8} \ &= \frac{35.16 + 58.91}{9.8} \ &= 9.60\ \text{s} \end{aligned} $$
The horizontal distance travelled in this time is
$$ \begin{aligned} x &= u_x t \ &= 82.85\times9.60 \ &= 795\ \text{m} \end{aligned} $$
so the suitcase lands about 795 m from the dog, in the direction of flight.
(b) The rock weighs $20\ \text{N}$, and at a height of $15\ \text{m}$ it is moving at $25\ \text{m/s}$ upward (take $g = 9.8\ \text{m/s}^2$). Its mass is $m = 20/9.8 = 2.04\ \text{kg}$. For the speed leaving the ground, apply energy conservation between the ground and the 15 m point,
$$ \begin{aligned} u^2 &= v^2 + 2gh \ &= 25^2 + 2(9.8)(15) \ u^2 &= 625 + 294 \ &= 919 \ u &= 30.3\ \text{m/s} \end{aligned} $$
The maximum height reached is then
$$ \begin{aligned} H &= \frac{u^2}{2g} \ &= \frac{919}{19.6} \ &= 46.9\ \text{m} \end{aligned} $$
So the rock leaves the ground at about 30.3 m/s and rises to about 46.9 m.
(c) A stone of mass $m = 0.8\ \text{kg}$ is whirled on a string of radius $r = 0.9\ \text{m}$ that breaks at a tension of $T = 600\ \text{N}$. The tension supplies the centripetal force, $T = \dfrac{mv^2}{r}$, so the maximum speed is
$$ \begin{aligned} v &= \sqrt{\frac{Tr}{m}} \ &= \sqrt{\frac{600\times0.9}{0.8}} \ v &= \sqrt{675} \ &= 26.0\ \text{m/s} \end{aligned} $$
The stone can be whirled at up to about 26 m/s before the string breaks.
(d) For a steel ball of radius $r = 2.00\ \text{mm} = 2\times10^{-3}\ \text{m}$ and density $\rho_s = 7800\ \text{kg/m}^3$ falling through castor oil of viscosity $\eta = 2.42\ \text{Ns/m}^2$ and density $\rho_l = 940\ \text{kg/m}^3$ (with $g = 9.8\ \text{m/s}^2$), Stokes' law gives the terminal velocity as
$$v = \frac{2}{9}\frac{r^2(\rho_s-\rho_l)g}{\eta}$$
Substituting the values,
$$ \begin{aligned} v &= \frac{2}{9}\frac{(2\times10^{-3})^2(7800-940)(9.8)}{2.42} \ v &= \frac{2}{9}\frac{(4\times10^{-6})(6860)(9.8)}{2.42} \ &= 0.0247\ \text{m/s} \end{aligned} $$
The terminal velocity is about 0.0247 m/s (roughly 2.5 cm/s).
Answer any two numerical questions: (a) Aluminium and brass rulers align at 0 C. How far apart are the 20.0 cm marks at 100 C (alpha_Al = 2.4x10^-5, alpha_brass = 2.0x10^-5 /K)? (b) A tank has 0.110 m^3 air at 3.4 atm; piston pulled to 0.390 m^3 at constant T. Find final pressure. (c) A diesel engine does 2200 J work and discards 4300 J heat per cycle. (i) Heat supplied? (ii) Thermal efficiency?
(a) The aluminium and brass rulers align at $0^\circ$C, with $\alpha_{Al} = 2.4\times10^{-5}$ and $\alpha_{brass} = 2.0\times10^{-5}\ \text{K}^{-1}$, and we want the gap between their $20.0\ \text{cm}$ marks at $100^\circ$C. Each mark shifts from the aligned left end by $L\alpha\Delta\theta$, so the separation of the two marks is their difference,
$$\Delta x = L(\alpha_{Al} - \alpha_{brass})\Delta\theta$$
Substituting the values,
$$ \begin{aligned} \Delta x &= 20(2.4\times10^{-5} - 2.0\times10^{-5})(100) \ \Delta x &= 20\times0.4\times10^{-5}\times100 \ &= 8\times10^{-3}\ \text{cm} \end{aligned} $$
So the 20.0 cm marks are about 0.008 cm (0.08 mm) apart.
(b) A tank holds $V_1 = 0.110\ \text{m}^3$ of air at $P_1 = 3.4\ \text{atm}$, and the piston is pulled out to $V_2 = 0.390\ \text{m}^3$ at constant temperature. The process is isothermal, so Boyle's law $P_1V_1 = P_2V_2$ applies,
$$ \begin{aligned} P_2 &= \frac{P_1V_1}{V_2} \ &= \frac{3.4\times0.110}{0.390} \ &= 0.959\ \text{atm} \end{aligned} $$
The final pressure is about 0.96 atm.
(c) A diesel engine does $W = 2200\ \text{J}$ of work and discards $Q_{out} = 4300\ \text{J}$ of heat per cycle. The heat supplied is the sum of these,
$$ \begin{aligned} Q_{in} &= W + Q_{out} \ &= 2200 + 4300 \ &= 6500\ \text{J} \end{aligned} $$
and the thermal efficiency is the work done per unit heat supplied,
$$ \begin{aligned} \eta &= \frac{W}{Q_{in}} \ &= \frac{2200}{6500} \ &= 0.338 \ &= 33.8% \end{aligned} $$
So the engine takes in 6500 J per cycle and runs at about 33.8% efficiency.
An optical fibre with refractive index 1.72 is surrounded by a glass coating of refractive index 1.50. Find the critical angle for total internal reflection at the fibre-glass interface.
An optical fibre of refractive index $n1 = 1.72$ is surrounded by a coating of refractive index $n2 = 1.50$. For light passing from the denser fibre into the less dense coating, the critical angle satisfies $$ \begin{aligned} \sin C &= ...
An electron (mass 9.1x10^-31 kg, charge 1.6x10^-19 C) is in a uniform electric field of 1.2x10^4 V/m. Find the time it takes to travel 1 cm from rest.
An electron of mass $m = 9.1\times10^{-31}\ \text{kg}$ and charge $q = 1.6\times10^{-19}\ \text{C}$ moves from rest through a uniform field $E = 1.2\times10^{4}\ \text{V/m}$ over a distance $s = 1\ \text{cm} = 0.01\ \text{m}$. The force on the electron is
$$ \begin{aligned} F &= qE \ &= (1.6\times10^{-19})(1.2\times10^{4}) \ &= 1.92\times10^{-15}\ \text{N} \end{aligned} $$
so its acceleration is
$$ \begin{aligned} a &= \frac{F}{m} \ &= \frac{1.92\times10^{-15}}{9.1\times10^{-31}} \ &= 2.11\times10^{15}\ \text{m/s}^2 \end{aligned} $$
Starting from rest, $s = \tfrac12 a t^2$, so the time taken is
$$ \begin{aligned} t &= \sqrt{\frac{2s}{a}} \ &= \sqrt{\frac{2(0.01)}{2.11\times10^{15}}} \ t &= \sqrt{9.48\times10^{-18}} \ &= 3.08\times10^{-9}\ \text{s} \end{aligned} $$
The electron takes about $3.08\times10^{-9}$ s (roughly 3.1 ns).
(a) Luminous intensity is the luminous flux emitted by a source per unit solid angle in a given direction:
Its SI unit is the candela (cd).
(b) A prism deviates light by an amount that depends on refractive index, which is larger for shorter wavelengths: . So violet is deviated most (bent most toward the base) and red least. With the usual orientation this places red at the top of the spectrum and violet at the bottom.
(a) Electrostatic shielding is the protection of a region from external electric fields by enclosing it in a conductor (a hollow conductor or cage). Since the field inside a conductor is zero, charges/fields outside cannot penetrate the cavity; this is why sensitive equipment is placed in a metal (Faraday) cage.
(b) On contact the charge redistributes until both reach the same potential. For two identical spheres the total charge shares equally, each getting . (For unequal conductors it distributes according to their capacitances to keep potentials equal.) If the charges were equal and opposite, they neutralise.
(a) Newton's laws: the first law (inertia), the second law (), and the third law (action equals reaction). For two colliding bodies with no external force, the third law makes the internal forces equal and o...
(a) Newton's law of cooling states that, for a small temperature excess, the rate at which a body loses heat is proportional to the difference between its temperature and that of its surroundings:
To find the specific heat capacity of a liquid by the cooling-curve method, equal volumes of the test liquid and of water (whose specific heat is known) are allowed to cool in the same calorimeter under identical surroundings through the same range of temperature. Since the rate of heat loss is fixed by the surroundings and is the same at each temperature, the times taken to cool are in the ratio of the heat capacities, and comparing these cooling times gives the liquid's specific heat capacity.
(b) A thermodynamic process is any change that takes a system from one state to another, such as an isothermal, adiabatic, isobaric or isochoric change. For an adiabatic expansion the gas follows , and the work done from to is
(c) Stefan's law says that the total energy radiated per unit area per unit time by a black body is proportional to the fourth power of its absolute temperature,
where the Stefan constant is . A perfect black body (one that absorbs every bit of radiation falling on it, ) cannot be made exactly, but a small hole in a hollow enclosure with blackened inner walls behaves almost like one: radiation entering the hole is reflected and absorbed again and again inside, so the hole absorbs (and emits) essentially as an ideal black body.
(a) For a prism (angle ), a ray refracts at both faces; the total deviation is with . At minimum deviation the ray passes symmetrically: and , so and
(a) The electric flux through a surface measures how many field lines cross it, defined as
Gauss's law states that the total flux out of any closed surface equals the enclosed charge divided by the permittivity of free space:
To find the field of an infinite plane sheet carrying surface charge density , we take a cylindrical pillbox (each flat face of area ) piercing the sheet. By symmetry the field comes straight out of both faces, so the flux is while the charge enclosed is :
Cancelling gives
which is independent of distance from the sheet.
(b) In a series combination every capacitor carries the same charge while the voltages add up:
Dividing through by gives the equivalent series capacitance,
In a parallel combination every capacitor has the same voltage while the charges add:
so dividing by gives
(a) The suitcase is released from a plane moving at at above the horizontal, from above the dog, with . It leaves with the plane's velocity, so its horizontal and vertical components are
Taking up as positive, the vertical motion from a height of gives
which rearranges to the quadratic
Solving for the positive root,
The horizontal distance travelled in this time is
so the suitcase lands about 795 m from the dog, in the direction of flight.
(b) The rock weighs , and at a height of it is moving at upward (take ). Its mass is . For the speed leaving the ground, apply energy conservation between the ground and the 15 m point,
The maximum height reached is then
So the rock leaves the ground at about 30.3 m/s and rises to about 46.9 m.
(c) A stone of mass is whirled on a string of radius that breaks at a tension of . The tension supplies the centripetal force, , so the maximum speed is
The stone can be whirled at up to about 26 m/s before the string breaks.
(d) For a steel ball of radius and density falling through castor oil of viscosity and density (with ), Stokes' law gives the terminal velocity as
Substituting the values,
The terminal velocity is about 0.0247 m/s (roughly 2.5 cm/s).
(a) The aluminium and brass rulers align at C, with and , and we want the gap between their marks at C. Each mark shifts from the aligned left end by , so the separation of the two marks is their difference,
Substituting the values,
So the 20.0 cm marks are about 0.008 cm (0.08 mm) apart.
(b) A tank holds of air at , and the piston is pulled out to at constant temperature. The process is isothermal, so Boyle's law applies,
The final pressure is about 0.96 atm.
(c) A diesel engine does of work and discards of heat per cycle. The heat supplied is the sum of these,
and the thermal efficiency is the work done per unit heat supplied,
So the engine takes in 6500 J per cycle and runs at about 33.8% efficiency.
An optical fibre of refractive index is surrounded by a coating of refractive index . For light passing from the denser fibre into the less dense coating, the critical angle satisfies $$ \begin{aligned} \sin C &= ...
An electron of mass and charge moves from rest through a uniform field over a distance . The force on the electron is
so its acceleration is
Starting from rest, , so the time taken is
The electron takes about s (roughly 3.1 ns).