A stem doubles a body's speed and asks what happens to its kinetic energy. The answer is four times, not twice. The square in the expression is easy to read past when you are moving quickly.
NCERT Class 11 Physics Chapter 5, page 73, defines kinetic energy as the energy a body possesses by virtue of its motion:
K = ½ m v²
Three properties follow directly from that expression, and questions on this topic almost always test one of them.
Quadratic in speed, linear in mass. Mass enters to the first power, speed to the second. Treble the speed and K rises ninefold; treble the mass and it merely trebles. Whenever a question gives you a ratio rather than numbers, square the speed ratio before you do anything else.
A non-negative scalar. Since v² ≥ 0 and m > 0, K can never be negative. A body travelling in the −x direction has positive kinetic energy, and a body at rest has exactly zero — zero is a legitimate value, not an undefined one. Kinetic energies of several bodies add as ordinary numbers; there is no direction to resolve.
Frame-dependent through v. The v in the formula is the speed measured in whichever frame you have chosen. A passenger seated in a moving train has zero kinetic energy for an observer in the train and a non-zero value for one on the platform. Both are correct.
Two conditions bound the expression: speeds must be non-relativistic (v much less than c), and it covers translational motion only — rotational kinetic energy is handled by a separate expression with moment of inertia and angular speed.
Kinetic energy also appears inside the work-energy theorem, collisions and power questions; each of those has its own lesson in this unit. Here the goal is narrower: make the expression and its scaling reflexes automatic. In the dossier's relevance data this topic carries medium weight in the chapter, with a skill mix of recall and single-step application and medium negative-marking risk.
Final watch-out: equal momentum does not mean equal kinetic energy. For a given momentum, the lighter body carries more.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
Which statement about kinetic energy is correct, as it is defined in NCERT Class 11 Physics Chapter 5?
Answer: A. In K = ½mv², mass is positive and v² is non-negative whatever the direction of motion, so K ≥ 0 always; the expression produces a single number with no direction. This follows from the definition on page 73 of NCERT Class 11 Physics Chapter 5.
Why B is wrong: B is wrong because squaring the velocity makes the sign of the direction irrelevant: (−v)² = v². A body moving in the −x direction has exactly the same positive kinetic energy as one moving at the same speed in the +x direction.
Why C is wrong: C is wrong because kinetic energy has no direction — the velocity is squared in K = ½mv², which destroys any directional information. Energy is a scalar.
Why D is wrong: D is wrong because the newton is the unit of force. Kinetic energy is measured in joules, as page 73 of the chapter states.
The expression K = ½mv² given in NCERT Class 11 Physics Chapter 5 applies to:
Answer: B. The chapter states the expression for the translational motion of a body in the non-relativistic regime (v much less than c); see page 73 of NCERT Class 11 Physics Chapter 5.
Why A is wrong: A is wrong because the expression is the non-relativistic form. At speeds approaching the speed of light it no longer holds and a relativistic expression is required — this is stated as a condition of use, not an optional refinement.
Why C is wrong: C is wrong because rotational kinetic energy is a separate quantity, written with moment of inertia and angular speed rather than mass and linear speed. The two are accounted for separately.
Why D is wrong: D is wrong because it imports restrictions that are not part of the definition. K = ½mv² is a property of the body's instantaneous speed alone; no assumption about the path or about the forces acting is involved.
In SI units, kinetic energy is measured in:
Answer: C. Kinetic energy is an energy, so its SI unit is the joule, as listed with the definition on page 73 of NCERT Class 11 Physics Chapter 5.
Why A is wrong: A is wrong because kilogram metre per second is the unit of momentum (mass × velocity), a different quantity that is a vector. Kinetic energy carries an extra factor of velocity and is a scalar.
Why B is wrong: B is wrong because the watt is the unit of power — energy per unit time. Confusing the two leaves the answer short by a factor of one second.
Why D is wrong: D is wrong because the newton is the unit of force. A force multiplied by a distance gives an energy in joules, so the newton alone cannot be an energy unit.
The speed of a car of fixed mass increases from 12 m/s to 24 m/s. Its kinetic energy becomes:
Answer: D. Kinetic energy varies as the square of the speed, so K₂/K₁ = (24/12)² = 2² = 4. The dependence on v² is explicit in the definition on page 73 of NCERT Class 11 Physics Chapter 5.
Why A is wrong: A is wrong because it reads the dependence as linear in speed — the error of carrying the speed ratio straight through without squaring it. K depends on v², so a factor of 2 in speed gives a factor of 4 in energy.
Why B is wrong: B is wrong because it squares the energy ratio a second time (4² = 16), applying the squaring step twice. Square the speed ratio once, then stop.
Why C is wrong: C is wrong because it cubes the speed ratio (2³ = 8). Nothing in K = ½mv² is cubic; the exponent on v is exactly 2.
A trolley of mass 2.0 kg moves along a level track at 3.0 m/s. Its kinetic energy is:
Answer: D. K = ½mv² = ½ × 2.0 × (3.0)² = 9.0 J, quoted to the two significant figures of the given data. The expression is the one defined on page 73 of NCERT Class 11 Physics Chapter 5.
Why A is wrong: A is wrong because it evaluates ½mv (3.0 J), dropping the square on the speed. Squaring is the step that turns this from a momentum-like quantity into an energy.
Why B is wrong: B is wrong because it evaluates mv (6.0 J) — the momentum in kg m/s, relabelled as an energy. Both the factor of ½ and the square have been lost.
Why C is wrong: C is wrong because it evaluates mv² (18 J), omitting the factor of ½. This is exactly twice the correct answer and is the most easily overlooked of the arithmetic slips here.
A block of mass 8.0 kg has a kinetic energy of 1.00 × 10² J. Its speed is:
Answer: C. Rearranging K = ½mv² gives v = √(2K/m) = √(2 × 100 / 8.0) = √25 = 5.0 m/s. The factor 2 and the square root both come directly from the defining expression on page 73 of NCERT Class 11 Physics Chapter 5.
Why A is wrong: A is wrong because it computes K/m = 100/8.0 = 12.5 — neither multiplying by 2 nor taking the square root. Two separate steps of the rearrangement have been skipped.
Why B is wrong: B is wrong because it stops at v² = 2K/m = 25 and reports that number as the speed. The units give the error away: 25 here is in m²/s², not m/s.
Why D is wrong: D is wrong because it takes √(K/m) = √12.5 ≈ 3.5, applying the square root but dropping the factor of 2 that comes from inverting the ½.
A passenger sits still in a carriage of a train that is moving at constant speed relative to the platform. One observer travels in the carriage and one stands on the platform; each computes the passenger's kinetic energy. Which statement is correct?
Answer: B. Kinetic energy is frame-dependent through v: relative to the carriage the passenger's speed is zero, relative to the platform it is the train's speed. Both values are correct in their own frame. The quantity is defined in terms of the body's speed on page 73 of NCERT Class 11 Physics Chapter 5.
Why A is wrong: A is wrong because being a scalar says only that the quantity has no direction — it says nothing about being the same in every frame. The speed v differs between frames, so K differs too.
Why C is wrong: C is wrong because it reverses the comparison: in the carriage frame the passenger's speed is zero, so the carriage observer records the smaller value, not the larger one.
Why D is wrong: D is wrong because zero is a perfectly good value of kinetic energy, not an undefined one. K ≥ 0, with equality for a body at rest in the chosen frame.
Two bodies, of masses m and 4m, move with momenta of equal magnitude. The ratio of the kinetic energy of the lighter body to that of the heavier body is:
Answer: A. Writing v = p/m and substituting into K = ½mv² gives K = p²/2m, so at equal p the kinetic energy is inversely proportional to mass: K_light/K_heavy = 4m/m = 4, that is 4 : 1. Both steps rest on the definition on page 73 of NCERT Class 11 Physics Chapter 5.
Why B is wrong: B is wrong because it makes K proportional to mass at fixed momentum, giving the ratio the wrong way round. Once p is fixed, the lighter body must be moving faster, and the v² term outweighs its smaller mass.
Why C is wrong: C is wrong because it assumes equal momentum implies equal kinetic energy. The two quantities depend differently on mass and speed — equality of one does not transfer to the other.
Why D is wrong: D is wrong because it carries the mass ratio 4 : 1 through as a square root (2 : 1), an extra root applied to a relation that is already linear in 1/m once p²/2m has been written.
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Given
Mass of a ball, m = 1.6 × 10⁻¹ kg.
Speed of the ball, v₁ = 2.5 × 10¹ m/s.
A second ball of the same mass moves at half that speed, v₂ = v₁/2.
Required
(a) The kinetic energy of the first ball.
(b) The ratio K₁ : K₂ of the two kinetic energies.
Concept
Kinetic energy is the energy a body has by virtue of its motion, and depends on the square of its speed (NCERT Class 11 Physics Chapter 5, page 73). Because mass is common to the two balls here, part (b) reduces to a comparison of v² alone — no numerical value of K₂ is needed.
Formula
K = ½ m v²
Substitution
K₁ = ½ × (1.6 × 10⁻¹ kg) × (2.5 × 10¹ m/s)²
For the ratio: K₁/K₂ = (½ m v₁²)/(½ m v₂²) = (v₁/v₂)² = (2)²
Calculation
(2.5 × 10¹)² = 6.25 × 10² m²/s²
K₁ = ½ × 1.6 × 10⁻¹ × 6.25 × 10² = 5.0 × 10¹ J
K₁/K₂ = 2² = 4
The factor ½ in K = ½mv² is an exact defining constant and the 2 in "half that speed" is an exact ratio; neither contributes to the significant-figure count. The precision of the answer is set by the two significant figures in m and v₁.
Final answer
(a) K₁ = 5.0 × 10¹ J (two significant figures).
(b) K₁ : K₂ = 4 : 1.
Note the scientific notation in (a): writing "50 J" would leave it ambiguous whether one or two significant figures are intended.
Common trap
Halving the speed is read as halving the energy, giving 2 : 1 instead of 4 : 1. The speed ratio must be squared before it is reported as an energy ratio. The same slip in reverse — squaring an energy ratio that has already been squared — produces 16 : 1. Square once, at the point where v enters.
Similar NEET-style question
A body of mass 4.0 × 10⁻¹ kg moves at 5.0 m/s. A second body of mass 8.0 × 10⁻¹ kg moves at 2.5 m/s. Find the ratio of their kinetic energies. *(Answer: K₁ : K₂ = 2 : 1 — the fourfold drop from halving the speed is only partly offset by the doubling of mass.)*
The kinetic energy K of a body of mass m moving with speed v is K = ½ m v². It is a scalar, always non-negative. Frame-dependent: depends on the choice of reference frame via the velocity. SI unit: joule.
-- NCERT Class 11 Physics, Ch. 5, p. 74Energy a body possesses by virtue of its motion. Always non-negative. Frame-dependent through v.
| Symbol | Quantity | SI Unit |
|---|---|---|
| K | Kinetic energy | J |
| m | Mass | kg |
| v | Speed | m/s |
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