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Laws of Motion
Physics · Class 11NCERT pp. 49–662 sets × 25 questions
Key facts and formulas for Laws of Motion, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Second law | F = dp/dt = m a; impulse J = F Δt = Δp |
| Third law | Action and reaction: equal, opposite, on different bodies, same kind |
| Momentum conservation | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ when no external force; K = p²/2m |
| Friction | f(s) ≤ μs N; f(k) = μk N; tan θ = μs at sliding; a(max) = μs g |
| Incline | a = g(sin θ − μ cos θ) down the slope; smooth: a = g sin θ |
| Circular motion | F = m v²/R; flat road v = √(μ R g); banked v = √(R g tan θ) |
| Lift | Up: R = m(g + a); down: R = m(g − a); free fall: R = 0 |
| Connected bodies | a = (m₂ − m₁)g/(m₁ + m₂); T = m₁(g + a) for the lighter mass |
| Springs | F = k x; series k = k₁k₂/(k₁ + k₂); parallel k = k₁ + k₂ |
| Momentum flow | F = (dm/dt) v for jets and bullets; rocket thrust = u (dm/dt) |
Three sample questions
Q1. Consider these statements.
I. Rest and uniform motion in a straight line both correspond to zero net external force.
II. Inertia is a force that keeps a body moving.
III. On a smooth surface a net force is needed to keep a body moving uniformly.
Which is correct?
- I and II only
- I only
- II and III only
- I and III only
Hint and solution
Hint: Newton's first law links zero net force to zero acceleration. Ask whether inertia is a force or a property, and whether friction is present on a smooth surface.
- Zero net force ⇔ zero acceleration — Rest and uniform straight-line motion both have constant velocity, so acceleration is zero and net force is zero. Statement I is true.
- Inertia is a property, not a force — Inertia is the tendency of a body to resist a change in its state. It does not push the body, so statement II is false.
- No friction → no force needed — On a smooth surface nothing opposes the motion, so the body keeps moving with no force. Statement III is false.
- Only I is correct — Only statement I is true. Option B.
Answer: B. Rest and uniform motion both have zero acceleration, so zero net force (I). Inertia is a property, not a force (II is false). With no friction no force is needed (III is false).
Q2. The momentum of a 5 kg body changes from 10 kg m/s to 30 kg m/s in 2 s along a line. The net force on it is
- 20 N
- 40 N
- 5 N
- 10 N
Hint and solution
Hint: Newton's second law in momentum form: force is the rate of change of momentum. The mass is extra information here.
- F = Δp / Δt — Newton's second law says the net force equals the rate of change of momentum.
- Δp = 30 − 10 = 20 kg m/s — Subtract the initial momentum from the final momentum.
- F = 20 / 2 = 10 N — Divide the change by the time of 2 seconds. The mass of 5 kg is not needed.
- Answer: 10 N — The net force is 10 newton. Option D.
Answer: D. F = change in momentum / time = (30 - 10)/2 = 10 N.
Q3. Assertion (A): A fielder draws his hands back while catching a fast ball.
Reason (R): This increases the time of stopping and so reduces the average force.
- Both A and R are true but R is not the correct explanation of A
- Both A and R are true and R is the correct explanation of A
- A is true but R is false
- A is false but R is true
Hint and solution
Hint: The momentum change of the ball is fixed. Think about what happens to F = Δp / t when t becomes larger.
- Δp of the ball is fixed — The ball must go from high speed to rest, so its momentum change cannot be altered by the fielder.
- F = Δp / t — Average force equals the momentum change divided by the stopping time.
- Larger t → smaller F — Drawing the hands back increases t, so the force on the hands is smaller and the hands are not hurt.
- A true, R true, R explains A — Both are true and R is the correct explanation. Option B.
Answer: B. The momentum change is fixed. A longer time gives a smaller F = change in p / t, which is exactly the reason.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.