NDA General Studies · Physics · 48 questions · 2017 to 2026
NDA Work, energy, power and gravitation previous year questions with solutions
Work, energy, power and gravitation is about one General Studies question in thirty, and its share has grown since 2023. The newer papers set numericals on energy conservation, g on other planets and escape speed beside the old one-fact items. Every question UPSC has set on it since 2017, solved. Grouped by the method each needs, newest first; open a question for its answer and worked solution.
2.1 Work: the definition, its sign and the joule (4)2.2 Energy: its forms, kinetic and potential energy, conservative forces and conservation of energy (9)2.3 The work-energy theorem and conservation of mechanical energy (11)2.4 Power, efficiency and simple machines (4)2.5 Newton's law of gravitation: G, the inverse square law, field and potential (8)2.6 Acceleration due to gravity, free fall, mass and weight (7)2.7 Satellites, Kepler's laws, escape speed and weightlessness (5)
2.1 Work: the definition, its sign and the joule
1. NDA 2025 (II)
The work done by the force acting on an object is zero if the displacement of the object
Answer and solution
Answer: (c) is in perpendicular direction of the direction of force
Method. W = Fs cosθ
Work is zero when θ = 90°, i.e. the displacement is perpendicular to the force (NCERT Class 9 Science ch 7 (Work and energy)).
2. NDA 2022 (I)
A mass M is dragged by a pulley on a horizontal plane by a force anti-parallel to its displacement. The work done in pulling the mass M is
Answer and solution
Answer: (d) negative
Method. Sign of work
The pulling force is anti-parallel to the displacement, θ = 180°, so W = Fs cos180° = -Fs, negative (NCERT Class 9 Science ch 7 (Work and energy)). (As worded, the stem is about a force opposing the displacement.)
3. NDA 2021 (II)
Work is said to be one Joule when a force of
Answer and solution
Answer: (a) 4 N moves an object by 25 cm.
Method. W = Fs; 1 J = 1 N·m
(a) 4 N × 0.25 m = 1 J. (b) gives 2 J, (c) 0.01 J, (d) 0.5 J (NCERT Class 9 Science ch 7 (Work and energy)).
4. NDA 2021 (II)
A negative work is done when an applied force F and the corresponding displacement S are
Answer and solution
Answer: (c) anti-parallel to each other.
Method. Sign of work W = Fs cosθ
Work is negative when θ = 180°, i.e. force and displacement are anti-parallel; perpendicular gives zero, parallel positive (NCERT Class 9 Science ch 7 (Work and energy)).
2.2 Energy: its forms, kinetic and potential energy, conservative forces and conservation of energy
5. NDA 2025 (II)
Which one of the following statements for the work done by gravity on a body is NOT correct?
Answer and solution
Answer: (c) Work done depends on the path followed by the body
Method. Gravity is a conservative force
Work done by gravity depends only on the vertical separation of the end points and not on path; so (c) is wrong. For horizontal displacement the force is perpendicular, W = 0 (NCERT Class 11 Physics ch 5 (Work, energy and power)).
6. NDA 2025 (II)
The energy is always conserved for a system which is
Answer and solution
Answer: (a) isolated only
Method. Conservation of energy for an isolated system
Energy of a system is conserved when no energy crosses its boundary, i.e. for an isolated system; a non-isolated one exchanges energy with the surroundings and its own energy can change, even though the total including surroundings is conserved (NCERT Class 11 Physics ch 5 (Work, energy and power)).
Keyed on the textbook sense that a system's energy is conserved only if isolated; (c) is arguable if 'system' includes surroundings.
7. NDA 2022 (I)
The energy possessed by a body due to its change in position or shape is called
Answer and solution
Answer: (b) potential energy
Method. Definition of potential energy
Energy due to position or configuration (shape) is potential energy; kinetic energy is due to motion (NCERT Class 9 Science ch 7 (Work and energy)).
8. NDA 2021 (II)
Fundamental laws of physics require
Answer and solution
Answer: (d) conservation of energy, momentum and charge.
Method. Fundamental conservation laws
Physics requires conservation of energy, linear momentum and charge together; the other options each deny one of them.
9. NDA 2021 (II)
Which one of the following is not a conservative force?
Answer and solution
Answer: (a) Frictional force
Method. Conservative vs dissipative force
Friction is non-conservative (work depends on path, energy is dissipated); electric, gravitational and spring forces are conservative (NCERT Class 11 Physics ch 5 (Work, energy and power)).
10. NDA 2019 (I)
Which one of the following energy is stored in the links between the atoms?
Answer and solution
Answer: (b) Chemical energy
Method. Chemical energy lies in bonds
Energy stored in the bonds linking atoms in molecules is chemical energy; nuclear energy sits in the nucleus.
11. NDA 2019 (I)
The correct sequence of energy transfer that occurs when an apple falls to the ground is
Answer and solution
Answer: (c) Gravitational potential energy → kinetic energy → heat energy to air → heat energy to ground and apple → sound energy
Method. Energy conversion in a fall
Stored gravitational PE becomes KE as it falls; air drag turns some into heat of the air; on impact the energy appears as heat in ground and apple and as sound (NCERT Class 9 Science ch 7 (Work and energy)).
12. NDA 2017 (II)
The force acting on a particle of mass m moving along the x-axis is given by F(x) = Ax2 - Bx. Which one of the following is the potential energy of the particle?
Answer and solution
Answer: (b) -x26(2Ax − 3B)
Method. U(x) = -∫F dx with U(0) = 0
U = -∫(Ax2 - Bx)dx = -(Ax33 − Bx22) = -x26(2Ax − 3B), taking U = 0 at x = 0 (NCERT Class 11 Physics ch 5 (Work, energy and power)).
13. NDA 2017 (II)
Which one of the following statements about energy is correct?
Answer and solution
Answer: (c) Energy can neither be created nor destroyed.
Method. Law of conservation of energy
Energy changes form but is neither created nor destroyed (NCERT Class 9 Science ch 7 (Work and energy)).
2.3 The work-energy theorem and conservation of mechanical energy
14. NDA 2026 (II)
The bob of a simple pendulum is displaced from its mean position and then released from rest 0.20 m above its mean position. What is the speed of the bob as it passes through the mean position? (Take g = 10 m/s2)
Answer and solution
Answer: (c) 2 m/s
Method. Energy conservation, mgh = ½mv2
v = √(2gh) = √(2.10.0.20) = √4 = 2 m/s (NCERT Class 11 Physics ch 5 (Work, energy and power)).
15. NDA 2026 (II)
A tennis ball of mass 350 g is thrown vertically upwards at a speed of 4 m/s. If M is the maximum gravitational potential energy of the ball and H is the maximum height it reaches, then which one of the following is correct? (Take g = 10 m/s2)
Answer and solution
Answer: (d) M = 2.8 J, H = 0.8 m
Method. Max height and PE at top
H = u2/2g = 16/20 = 0.8 m; M = mgH = 0.35.10.0.8 = 2.8 J (equal to ½mu2 = 0.5.0.35.16 = 2.8 J) (NCERT Class 11 Physics ch 5 (Work, energy and power)).
16. NDA 2026 (II)
A particle of mass m moves along x-direction under the force F(x) = F0 (1 − xL) for 0 ≤ x ≤ L. If the particle starts from rest at x = 0, then what is the speed (v) of the particle at x = L?
Answer and solution
Answer: (b) v = √(F0Lm)
Method. Work–energy theorem with variable force
W = ∫0LF0(1 − x/L)dx = F0(L − L/2) = F0L/2 = ½mv2, so v = √(F0L/m) (NCERT Class 11 Physics ch 5 (Work, energy and power)).
17. NDA 2026 (I)
A ball is dropped from rest from height h above the ground in frame S (the Earth's frame). Another frame S′ is moving upwards with constant speed u relative to the Earth. In frame S′, the ball has initial downward speed v. Pertaining to the change in kinetic energy (ΔK) of the ball from release to just before hitting the ground as measured in frames S and S′ separately, which one of the following is correct?
Answer and solution
Answer: (c) ΔK is larger in frame S′.
Method. Work–energy theorem in two frames; ΔK is frame dependent
S: t = √(2h/g), ΔK = mgh. In S′ the ball starts at speed u (v = u) downward and during t the ball's displacement is h + ut (the frame moves up). W = mg(h + ut) so ΔK′ = mgh + mgut > mgh. Check: ½m(u + gt)2 - ½mu2 = mugt + ½mg2t2 = mgut + mgh. So ΔK is larger in S′ (NCERT Class 11 Physics ch 5 (Work, energy and power)).
18. NDA 2026 (I)
A particle is moved from point X to point Y under a force field. The work done depends only on the initial and final speeds. Which one of the following is correct?
Answer and solution
Answer: (b) The net work equals the change in kinetic energy.
Method. Work–energy theorem
Work done equals change in kinetic energy ½mvf2 - ½mvi2, which depends only on initial and final speeds for any force; that gives (b). It does not show the force is conservative (a), constant (c), or that speed rises (d) (NCERT Class 11 Physics ch 5 (Work, energy and power)).
19. NDA 2025 (II)
Suppose, a ball of mass M is thrown upwards from a point A and it reaches up to the highest point B and returns back to point A, which one among the following is correct?
Answer and solution
Answer: (a) Kinetic Energy at A = Potential Energy at B
Method. Mechanical energy conservation
Taking PE zero at A and neglecting air, all KE at A converts to PE at B: KEA = PEB. At B the KE is zero, at A the PE is zero (NCERT Class 11 Physics ch 5 (Work, energy and power)).
20. NDA 2024 (II)
There is a ball of mass 320 g. It has 625 J potential energy when released freely from a height. The speed with which it will hit the ground is
Answer and solution
Answer: (a) 62.5 m/s
Method. Energy conservation, PE → KE
m = 0.32 kg; ½mv2 = 625 ⇒ v = √(2.625/0.32) = √3906.25 = 62.5 m/s (NCERT Class 11 Physics ch 5 (Work, energy and power)).
21. NDA 2024 (I)
A block of mass 2 kg, moving with the initial speed of 3 m/s comes to rest on a rough horizontal surface after travelling a distance of 3 m. The magnitude of the frictional force is:
Answer and solution
Answer: (b) 3 N
Method. Work–energy theorem
F·s = ½mu2: F = (½·2.9)/3 = 3 N (NCERT Class 11 Physics ch 5 (Work, energy and power)). Check: a = u2/2s = 1.5 m/s2, F = 2.1.5 = 3 N.
22. NDA 2023 (I)
Two identical containers X and Y are connected at the bottom by a thin tube of negligible volume. The tube has a valve in it, as shown in the figure. Initially container X has a liquid filled up to height h in it and container Y is empty. When the valve is opened, both containers have equal amount of liquid in equilibrium. If the initial (before the valve is opened) potential energy of the liquid is P1 and the final potential energy is P2 then:
Answer and solution
Answer: (c) P1 = 2P2
Method. PE of a liquid = m g × height of its centre of mass
Initially: mass m with centre of mass at h/2, P1 = mgh/2. Final: containers identical, so liquid stands at h/2 in each; each holds m/2 with centre of mass at h/4, P2 = 2·(m/2)g(h/4) = mgh/4. P1/P2 = 2, so P1 = 2P2; the rest of the energy is dissipated as heat (NCERT Class 11 Physics ch 5 (Work, energy and power)).
23. NDA 2021 (II)
An object of mass 2000 g possesses 100 J kinetic energy. The object must be moving with a speed of
Answer and solution
Answer: (a) 10.0 m/s
Method. K = ½mv2
m = 2000 g = 2 kg; v = √(2K/m) = √(2.100/2) = √100 = 10.0 m/s (NCERT Class 11 Physics ch 5 (Work, energy and power)).
24. NDA 2019 (II)
A rigid body of mass 2 kg is dropped from a stationary balloon kept at a height of 50 m from the ground. The speed of the body when it just touches the ground and the total energy when it is dropped from the balloon are respectively
(acceleration due to gravity = 9.8 m/s2)
(acceleration due to gravity = 9.8 m/s2)
Answer and solution
Answer: (d) √980 m.s-1 and 980 J
Method. Energy conservation in free fall
v = √(2gh) = √(2.9.8.50) = √980 m/s. Total energy at release (at rest, 50 m above ground, ground as reference) = mgh = 2.9.8.50 = 980 J. Both match (d).
2.4 Power, efficiency and simple machines
25. NDA 2026 (I)
A constant power machine pulls a block on a smooth horizontal surface. Which one of the following correctly describes the relation between speed of the block (v) and time (t)?
Answer and solution
Answer: (b) v ∝ √t
Method. P = Fv = d(½mv2)/dt
Constant power: ½mv2 = Pt, so v = √(2Pt/m) ∝ √t (NCERT Class 11 Physics ch 5 (Work, energy and power)).
26. NDA 2024 (II)
Which one of the following sketches correctly describes a lever of second class?
Answer and solution
Answer: (c) [sketch (c); see figure]
Method. Second-class lever: load between fulcrum and effort
In (c) the fulcrum is at the left end, the load acts in the middle and the effort at the right end, which is a second class lever. (a) fulcrum lies between load and effort (first class), (b) first class, (d) effort lies between fulcrum and load (third class).
27. NDA 2023 (I)
The power required to lift a mass of 8.0 kg up a vertical distance of 4 m in 2 s is (taking acceleration due to gravity as 10 m/s2):
Answer and solution
Answer: (b) 160 W
Method. P = mgh/t
Work = 8.10.4 = 320 J; P = 320/2 = 160 W (NCERT Class 9 Science ch 7 (Work and energy)).
28. NDA 2023 (I)
Which one of the following is an example of Second Class Lever?
Answer and solution
Answer: (b) A bottle opener
Method. Classes of lever
In a second-class lever the load lies between fulcrum and effort. A bottle opener rests on the cap edge (fulcrum), the cap is the load, and the hand applies effort further out. Scissors are first class; a cricket bat and a bow are third class (effort between).
2.5 Newton's law of gravitation: G, the inverse square law, field and potential
29. NDA 2026 (II)
Consider the following:
I. Gravitational field due to a spherical body
II. Electrostatic field due to a point charge
III. Strong nuclear force field due to a proton
IV. Magnetic field due to a bar magnet
How many of the above follow the inverse square law?
I. Gravitational field due to a spherical body
II. Electrostatic field due to a point charge
III. Strong nuclear force field due to a proton
IV. Magnetic field due to a bar magnet
How many of the above follow the inverse square law?
Answer and solution
Answer: (b) Two
Method. Which fields obey 1/r2
Gravitational field of a sphere (outside) and electrostatic field of a point charge follow 1/r2. The strong nuclear force is short range, not inverse-square. A bar magnet's field is dipolar, ∝ 1/r3 on axis. So two (NCERT Class 11 Physics ch 7 (Gravitation)).
30. NDA 2026 (I)
For an object in gravitational field, the gravitational potential is the same at two points A and B, but the gravitational field is not the same at these two points. Which one of the following statements is correct?
Answer and solution
Answer: (d) No work is done by gravity in moving the object from point A to point B.
Method. W = m(VA - VB)
Work by gravity between A and B = -m·ΔV; equal potentials give zero work, so (d). Different fields at the two points do not matter; gravity is still conservative (NCERT Class 11 Physics ch 7 (Gravitation)).
31. NDA 2024 (II)
The masses of two planets are in the ratio of 1 : 7. The ratio between their diameters is 2 : 1. The ratio of forces which they exert on each other is
Answer and solution
Answer: (c) 1 : 1
Method. Newton's third law
The two planets exert gravitational forces on each other that are equal in magnitude and opposite in direction whatever their masses and sizes, so ratio 1 : 1 (NCERT Class 11 Physics ch 7 (Gravitation)). (Direct check: F = Gm1m2/r2, same for both.)
32. NDA 2024 (I)
LIGO experiment confirmed one of the predictions of:
Answer and solution
Answer: (d) General theory of relativity
Method. LIGO and gravitational waves
LIGO detected gravitational waves in 2015, predicted by Einstein's general theory of relativity.
33. NDA 2019 (II)
Two bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M each are placed R2 distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies in the second system will be
Answer and solution
Answer: (a) 16 F
Method. Inverse-square law
F = GM2/R2; second system F′ = G(2M)2/(R/2)2 = 4.4·GM2/R2 = 16F (NCERT Class 11 Physics ch 7 (Gravitation)).
34. NDA 2019 (I)
'Black hole' is a
Answer and solution
Answer: (c) star which has collapsed into itself and has large acceleration due to gravity on its surface
Method. Definition of black hole
A black hole is a star collapsed into itself to very small radius, so g = GM/R2 on its surface is enormous, large enough that even light cannot escape; (a) and (d) wrongly say zero.
35. NDA 2018 (I)
Which one of the following statements about gravitational force is NOT correct?
Answer and solution
Answer: (d) It is same for all pairs of bodies in our universe
Method. Dependence of gravitational force on masses and distance
F = Gm1m2/r2 differs from pair to pair with masses and separation, so (d) is not correct. (a) holds for all bodies, (b) it dominates between celestial bodies, (c) it is negligible between atoms because the masses are tiny (NCERT Class 11 Physics ch 7 (Gravitation)).
36. NDA 2017 (I)
Which one of the following statements is true for the relation F = Gm1m2r2?
(All symbols have their usual meanings)
(All symbols have their usual meanings)
Answer and solution
Answer: (d) The quantity G is a universal constant.
Method. Universal gravitational constant
G is the same in the law of gravitation for any two masses anywhere, hence a universal constant; it does not depend on g (g is derived from it: g = GM/R2), does not vary with place, and is not restricted to the Earth (NCERT Class 11 Physics ch 7 (Gravitation)).
2.6 Acceleration due to gravity, free fall, mass and weight
37. NDA 2026 (II)
Consider the following statements:
I. The weight of an object is the same everywhere on the surface of the Earth, but its inertial mass could be different.
II. The inertial mass and gravitational mass of an object are proportional and the proportionality constant is the same everywhere.
III. The inertial mass and weight of an object are the same at different places on Earth.
Which of the statements given above is/are correct?
I. The weight of an object is the same everywhere on the surface of the Earth, but its inertial mass could be different.
II. The inertial mass and gravitational mass of an object are proportional and the proportionality constant is the same everywhere.
III. The inertial mass and weight of an object are the same at different places on Earth.
Which of the statements given above is/are correct?
Answer and solution
Answer: (b) II only
Method. Inertial mass, gravitational mass, weight
I is false: weight mg varies slightly with place, mass does not. II is true: gravitational and inertial mass are proportional with one universal constant (equivalence principle). III is false: weight changes with g (NCERT Class 11 Physics ch 7 (Gravitation)).
38. NDA 2026 (II)
A narrow tunnel passes through the centre of a planet of radius R and uniform mass density ρ. A particle is released into the tunnel. What is the angular frequency of oscillation of the particle (ω) equal to? (Symbols carry their usual meaning)
Answer and solution
Answer: (a) ω = √(4πGρ3)
Method. SHM inside a uniform planet
Inside, g(r) = 43πGρ r, so acceleration = -(4πGρ3)x, and ω = √(4πGρ/3) (NCERT Class 11 Physics ch 7 (Gravitation)).
39. NDA 2025 (I)
Two bodies of unequal masses are dropped from a tower. At any instant, they have equal
Answer and solution
Answer: (b) Acceleration
Method. Free fall
Both fall with a = g regardless of mass. Momentum, PE and KE all scale with mass so differ (NCERT Class 9 Science ch 6 (Gravitation)).
40. NDA 2019 (I)
Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1 > R2. The accelerations due to gravity on the surface of these planets are related as
Answer and solution
Answer: (a) g1 > g2
Method. g = 43πGρR
With equal density g ∝ R, so R1 > R2 gives g1 > g2 (NCERT Class 11 Physics ch 7 (Gravitation)).
41. NDA 2018 (II)
A planet has a mass M1 and radius R1. The value of acceleration due to gravity on its surface is g1. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?
Answer and solution
Answer: (c) g1/2
Method. g = GM/R2
g2 = G(2M1)/(2R1)2 = 24g1 = g1/2 (NCERT Class 11 Physics ch 7 (Gravitation)).
42. NDA 2018 (I)
Which one of the following statements about the mass of a body is correct?
Answer and solution
Answer: (b) It is same everywhere
Method. Mass is an invariant property of matter
Mass is a measure of the quantity of matter/inertia and is the same everywhere, unlike weight, which changes with g (b) (NCERT Class 9 Science ch 6 (Gravitation)). Option (d) is true only in classical physics: strictly a heated body gains mass E/c2, so (b) is the one sound statement; (a) and (c) are false.
Keep (b); note that (d) is also true at school level, so this rests on the strict mass-energy reading.
43. NDA 2017 (II)
In vacuum, a five-rupee coin, a feather of sparrow and a mango are dropped simultaneously from the same height. The time taken by them to reach the bottom is t1, t2 and t3 respectively. In this situation, we will observe that
Answer and solution
Answer: (d) t1 = t2 = t3
Method. Free fall in vacuum is independent of mass
With no air, every body falls with a = g, so t = √(2h/g) is the same: t1 = t2 = t3 (NCERT Class 9 Science ch 6 (Gravitation)).
2.7 Satellites, Kepler's laws, escape speed and weightlessness
44. NDA 2026 (I)
One year at a planet is 8 times as large as compared to the one year at the Earth. Which one of the following is correct about the planet's orbit?
Answer and solution
Answer: (d) The semimajor axis of the planet's orbit is four times as compared to that of the Earth.
Method. Kepler's third law T2 ∝ a3
a3 = T2 = 64 (in Earth units), a = 4 times the Earth's (NCERT Class 11 Physics ch 7 (Gravitation)).
45. NDA 2024 (II)
An astronaut whose weight on the Earth is 600 N experiences weightlessness on International Space Station orbiting around the Earth. It means that
Answer and solution
Answer: (b) normal reaction of the space-station floor on the astronaut is zero
Method. Weightlessness = zero normal reaction
The station and astronaut are in free fall with the same acceleration g', so the floor exerts no reaction (apparent weight is zero). Gravity still acts (nearly its surface value), the acceleration is not zero, and no centrifugal force is needed in the inertial view (NCERT Class 11 Physics ch 7 (Gravitation)).
46. NDA 2024 (I)
Escape speed from the Earth is close to 11.2 km s-1. On another planet whose radius is half of the Earth's radius and whose mass density is four times that of the Earth, the escape speed in km s-1 will be close to:
Answer and solution
Answer: (a) 11.2
Method. ve = √(2GM/R) = R√(8πGρ/3)
ve ∝ R√ρ, so v'/v = (1/2)·√4 = 1; escape speed stays 11.2 km/s (NCERT Class 11 Physics ch 7 (Gravitation)).
47. NDA 2020 (I)
Two planets orbit the Sun in circular orbits, with their radius of orbit as R1 = R and R2 = 4R. Ratio of their periods (T1/T2) around the Sun will be
Answer and solution
Answer: (b) 1/8
Method. Kepler's law of periods T2 ∝ R3
T1/T2 = (R1/R2)3/2 = (1/4)3/2 = 1/8 (NCERT Class 11 Physics ch 7 (Gravitation)).
48. NDA 2017 (II)
Which one of the following statements about a satellite orbiting around the Earth is correct?
Answer and solution
Answer: (d) Satellite does not require any energy for orbiting.
Method. Orbit needs only gravity as centripetal force
Gravity supplies the centripetal force m v2/r, and no drag acts in space, so no energy is spent to keep it in orbit; fuel and solar panels serve manoeuvres and instruments, not orbiting (NCERT Class 11 Physics ch 7 (Gravitation)).
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