Q.Write Newton's second law of motion, and on its basis prove that Force = mass x acceleration. OR From where does a car moving on a level (plane) circular road obtain the centripetal force? Establish the expression for the maximum speed of the car on this road.
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Newton's Second Law: The Law That Connects Force and Motion
Imagine you're pushing a shopping cart. If you push gently, it moves slowly. Push harder, and it speeds up faster. Now imagine the cart is full of groceries — even with the same push, it accelerates much more slowly than an empty cart. This everyday experience is exactly what Newton's Second Law captures.
The Intuition First
Two things matter when you push something:
- How hard you push — the force you apply.
- How heavy the object is — its mass.
The harder you push, the more the object speeds up. The heavier the object, the less it speeds up for the same push. So acceleration depends on both force and mass — and in opposite ways.
"Acceleration" here means any change in velocity — speeding up, slowing down, or changing direction. It's not just "going faster."
The Precise Statement
Newton's Second Law says:
The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The acceleration is in the same direction as the net force.
In one equation:
a=mFnet
Or more commonly:
Fnet=ma
Where:
- Fnet is the net force (the vector sum of all forces acting on the object) — measured in newtons (N)
- m is the mass of the object — measured in kilograms (kg)
- a is the acceleration — measured in metres per second squared (m/s2)
Fnet=ma
What This Really Means
Force causes acceleration, not velocity. A constant net force produces constant acceleration — meaning the velocity keeps changing at a steady rate. If you stop pushing, the net force becomes zero, and acceleration becomes zero (the object continues at constant velocity — that's Newton's First Law).
Mass is a measure of inertia. The more mass an object has, the harder it is to change its motion. A truck needs a much larger force than a bicycle to achieve the same acceleration.
Direction matters. Force and acceleration are vectors — they point the same way. If you push north, the acceleration is north. If multiple forces act, you must add them as vectors to find the net force.
A Simple Example
A 2 kg block is pushed with a net force of 10 N to the right.
a=mFnet=2 kg10 N=5 m/s2
The block accelerates at 5 m/s2 to the right. Every second, its velocity increases by 5 m/s in that direction. …
Newton's second law directly leads to the familiar equation F = ma once mass is treated as constant. …
Newton's second law: F is proportional to dp/dt. For constant mass, this reduces to F = ma.
Newton's Second Law of Motion states: The rate of change of momentum of a body is directly proportional to the applied external force, and this change takes place in the direction of the applied force.
Mathematically: F is proportional to dp/dt
i.e., F = k (dp/dt), where k is a constant of proportionality (k = 1 in SI units with the newton defined appropriately).
Now, momentum p = mv. For a body of constant mass m:
dp/dt = d(mv)/dt = m (dv/dt) = ma
(since dv/dt = a, the acceleration).
So: F = ma
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Showing the 12 most recent of 17 on this concept.
- CBSE 2026Set ANNUAL1 markQ.Write the mathematical equation of Newton's Second Law.
›Reveal solutionSolution
Newton's Second Law: the net force on a body equals the rate of change of its momentum, F = dp/dt, which reduces to F = ma for constant mass.
Newton's second law states that the rate of change of momentum of a body is directly proportional to the applied net force and takes place in the direction of that force:
F = dp/dt, where p = mv is momentum. …
- CBSE 2026Set ANNUAL1 markMCQQ.What is the mass of a body that accelerates at a rate of 3.3 m/s^2 with a force of 120 N?(a) 44.36 kg(b) 36.36 kg(c) 54.36 kg(d) None of these
›Reveal solutionSolution
Newton's second law, F = ma, rearranged gives m = F/a; plugging in the numbers gives about 36.36 kg.
Newton's second law: F = m a
Given F = 120 N, a = 3.3 m/s^2
…
- CBSE 2026Set ANNUAL1 markMCQQ.Match the column - select the correct definition (from Column B) for the term 'Force' (Column A):(a) change in linear momentum(b) motion opposing force(c) loss of energy(d) rate of change of momentum(e) ability of doing work(f) rate of doing work
›Reveal solutionSolution
By Newton's second law, force is the rate of change of momentum.
Newton's second law of motion defines force as the time rate of change of a body's linear momentum:
F = dp/dt …
- CBSE 2026Set ANNUAL1 markMCQQ.The direction of force is always(a) along the velocity(b) opposite to the velocity(c) perpendicular to the velocity(d) parallel to the acceleration
›Reveal solutionSolution
Newton's second law F = ma makes force parallel to acceleration. Answer (D).
Newton's second law states F = ma. Since mass m is a positive scalar, the force vector and the acceleration vector always point in the same direction; the force is parallel to the acceleration.
…
- CBSE 2025Set ANNUAL1 markMCQQ.Newton's second law of motion is(a) F = dp/dt(b) F = mv(c) F = mv^2(d) F = m^2 v
›Reveal solutionSolution
Newton's second law of motion, in its most general form, is F = dp/dt (rate of change of momentum), which reduces to F = ma only when mass is constant.
Newton's second law states that the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force. With the proportionality constant taken as 1 in SI units:
F = dp/dt
…
- CBSE 2025Set ANNUAL1 markMCQQ.A force vector applied on a mass is represented as F=(6i^−8j^+10k^)N and accelerates the mass with 1 ms−2. What will be the mass of the body?(a) 102 kg(b) 210 kg(c) 10 kg(d) 20 kg
›Reveal solutionSolution
Newton's second law gives ∣F∣=ma, so m=∣F∣/a; the magnitude of the force vector is found from its components.
F=(6i^−8j^+10k^)N
∣F∣=62+(−8)2+102=36+64+100=200=102 N
…
- CBSE 2024Set ANNUAL1 markMCQQ.Which of the following quantities of a body remains constant under uniform force acting on it? (A) Velocity (B) Acceleration (C) Momentum (D) Kinetic energy
›Reveal solutionSolution
Under a constant force, acceleration alone stays constant; velocity, momentum, KE all change.
By Newton's second law F=ma, so a=F/m. If the force F and mass m are both constant, the acceleration is constant. However, since the body keeps accelerating, its velocity v=u+at keeps increasing, momentum p=mv …
- CBSE 2024Set ANNUAL1 markMCQQ.The linear momentum of a body changes at the rate of 10 kgms−1 per second. What is the force acting on the body?(a) 1N(b) 10N(c) 1 Kgf(d) 60m
›Reveal solutionSolution
Newton's second law states F=dtdp; here the rate is given directly as 10kgms−1 per second.
Newton's second law of motion states that the force acting on a body equals the rate of change of its linear momentum: F=dtdp. It is given that the momentum changes at the rate of 10kgms−1 per second, …
- CBSE 2024Set ANNUAL1 markQ.Fill in the blank: The rate of change of ______ of a body is directly proportional to the applied force.
›Reveal solutionSolution
Newton's second law states that the rate of change of momentum is directly proportional to the applied force: F is proportional to dp/dt.
Momentum p of a body is defined as p = mv, the product of its mass and velocity. Newton's second law of motion states that the net external force acting on a body equals (is directly proportional to, and in SI units equal to) the rate of change of its momentum: …
- CBSE 2024Set ANNUAL1 markQ.Match the term with its correct dimensional formula / equation from this pool (each option is used exactly once):(a) [M0LT-2],(b) [MLT-2],(c) S = ut + (1/2)at^2,(d) [M-1L3T-2],(e) v = u + at,(f) [MLT-1]. Which option correctly matches 'Force'?
›Reveal solutionSolution
Force = mass x acceleration, so its dimensions are [M][LT^-2] = [MLT^-2], matching option (b).
Force is defined by Newton's second law as F = ma. Mass has dimension [M], and acceleration has dimension [LT^-2] (rate of change of velocity, itself rate of change of displacement). …
- CBSE 2023Set ANNUAL1 markMCQQ.A body of mass 2 kg travels according to the law x(t) = pt + qt^2 + rt^3, where p = 3 ms^-1, q = 4 ms^-2 and r = 5 ms^-3. The force acting on the body at t = 2 seconds is(a) 68N(b) 134N(c) 158N(d) 136N
›Reveal solutionSolution
Differentiate x(t) twice to get a(t), then use F = ma. At t = 2 s, F = 136 N (option d).
Given x(t) = pt + qt^2 + rt^3, with p = 3 m/s, q = 4 m/s^2, r = 5 m/s^3, and mass m = 2 kg.
Step 1: Find velocity by differentiating position once.
v(t) = dx/dt = p + 2qt + 3rt^2.
Step 2: Find acceleration by differentiating velocity once (i.e., position twice).
a(t) = dv/dt = 2q + 6rt.
Step 3: Substitute t = 2 s.
a(2) = 2(4) + 6(5)(2) = 8 + 60 = 68 m/s^2.
…
- CBSE 2023Set ANNUAL1 markQ.Answer in one word/sentence: Give the relation between the MKS and CGS unit of force.
›Reveal solutionSolution
1 Newton (MKS/SI unit of force) equals 10^5 dyne (CGS unit of force).
1 Newton = 1 kg x 1 m/s^2
Convert kg to g: 1 kg = 1000 g = 10^3 g
Convert m to cm: 1 m = 100 cm = 10^2 cm
So: 1 N = 10^3 g x 10^2 cm/s^2 = 10^5 g cm/s^2
…
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