newton-s-second-law-and-momentum MCQs for UPSC Prelims

25 practice questions on newton-s-second-law-and-momentum from the How Forces Affect Motion section of the UPSC Prelims syllabus. 25 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

7 Easy 12 Medium 6 Hard

Sample questions

Q1
medium
An object of mass $3\ \text{kg}$ has a momentum of $12\ \text{kg m s}^{-1}$ as it moves along a straight line. How fast is it moving?
  1. A $0.25\ \text{m s}^{-1}$
  2. B $4\ \text{m s}^{-1}$
  3. C $9\ \text{m s}^{-1}$
  4. D $36\ \text{m s}^{-1}$
Show answer and explanation

Correct answer: B - $4\ \text{m s}^{-1}$

Since momentum is mass multiplied by velocity, the velocity is $12 \div 3 = 4\ \text{m s}^{-1}$. Multiplying instead of dividing gives $36$, and dividing the wrong way round gives $0.25$. Subtracting the mass from the momentum gives $9$, which mixes two quantities that are not even measured in the same unit.
Q2
medium
A steady unbalanced force acts on a trolley for $4\ \text{s}$ and changes its momentum from $6\ \text{kg m s}^{-1}$ to $22\ \text{kg m s}^{-1}$ in the same direction. How large is the force?
  1. A $5.5\ \text{N}$
  2. B $16\ \text{N}$
  3. C $1.5\ \text{N}$
  4. D $4\ \text{N}$
Show answer and explanation

Correct answer: D - $4\ \text{N}$

The momentum changes by $22 - 6 = 16\ \text{kg m s}^{-1}$ in $4\ \text{s}$, so the force is $16 \div 4 = 4\ \text{N}$. Quoting $16\ \text{N}$ stops at the change in momentum and forgets to divide by the time. Dividing the final momentum by the time gives $5.5$, and dividing the starting momentum by the time gives $1.5$; both use one reading instead of the change.
Q3
easy
A net force of $24\ \text{N}$ acts on a block of mass $6\ \text{kg}$ lying on a smooth horizontal surface. What acceleration does the block get?
  1. A $144\ \text{m s}^{-2}$
  2. B $0.25\ \text{m s}^{-2}$
  3. C $4\ \text{m s}^{-2}$
  4. D $30\ \text{m s}^{-2}$
Show answer and explanation

Correct answer: C - $4\ \text{m s}^{-2}$

Rearranging $F = ma$ gives $a = 24 \div 6 = 4\ \text{m s}^{-2}$. Multiplying the force by the mass gives $144$, and dividing the mass by the force gives $0.25$. Adding force and mass gives $30$, which has no physical meaning.
Q4
medium
Newton's second law of motion states that
  1. A the change in momentum of an object is equal to the unbalanced force acting on it, whatever the time taken
  2. B the momentum of an object is proportional to the unbalanced force acting on it
  3. C the unbalanced force on an object is proportional to its momentum divided by its mass
  4. D the rate of change of momentum of an object is proportional to the unbalanced force acting on it, and takes place along the direction of that force
Show answer and explanation

Correct answer: D - the rate of change of momentum of an object is proportional to the unbalanced force acting on it, and takes place along the direction of that force

The law links force to how quickly momentum changes, not to momentum itself, and it also fixes the direction of that change. A steady force acting for a long time keeps changing the momentum, so momentum cannot simply be proportional to the force. The time taken matters, since the same change made more slowly needs a smaller force. Momentum divided by mass is just velocity, which is not what a force is proportional to.
Q5
easy
In which direction does the momentum of a moving object point?
  1. A In the same direction as its velocity
  2. B Momentum has no direction, only a size
  3. C In the direction opposite to its velocity
  4. D Always vertically downward, in the direction of its weight
Show answer and explanation

Correct answer: A - In the same direction as its velocity

Momentum is the mass, which is a plain positive number, multiplied by the velocity, so it points exactly the way the object is moving. Pointing the opposite way would describe an object travelling backwards. Weight always acts downward but has nothing to do with the direction of motion, and a quantity with mass and velocity in it certainly carries a direction.
Q6
hard
A full sack of rice has a weight of $245\ \text{N}$. Three such sacks are stacked on a weighing platform. Taking $g = 9.8\ \text{m s}^{-2}$, what total mass rests on the platform?
  1. A $25\ \text{kg}$
  2. B $75\ \text{kg}$
  3. C $245\ \text{kg}$
  4. D $735\ \text{kg}$
Show answer and explanation

Correct answer: B - $75\ \text{kg}$

One sack has a mass of $245 \div 9.8 = 25\ \text{kg}$, so three of them come to $75\ \text{kg}$. Quoting $25\ \text{kg}$ gives the mass of a single sack and forgets the other two. Writing $245\ \text{kg}$ or $735\ \text{kg}$ takes the weight of one sack or of all three and simply relabels newtons as kilograms.
Q7
hard
A van of mass $900\ \text{kg}$ has to increase its speed uniformly from $10\ \text{m s}^{-1}$ to $25\ \text{m s}^{-1}$ in $6\ \text{s}$ along a straight road. What net forward force is needed?
  1. A $3750\ \text{N}$
  2. B $13500\ \text{N}$
  3. C $1500\ \text{N}$
  4. D $2250\ \text{N}$
Show answer and explanation

Correct answer: D - $2250\ \text{N}$

The speed rises by $25 - 10 = 15\ \text{m s}^{-1}$ in $6\ \text{s}$, so the acceleration is $2.5\ \text{m s}^{-2}$ and the force is $900 \times 2.5 = 2250\ \text{N}$. Using the final speed alone gives $3750\ \text{N}$ and using the starting speed alone gives $1500\ \text{N}$, because both ignore that only the change in speed matters. The value $13500\ \text{N}$ forgets to divide by the time.
Q8
easy
What net force must be applied to a trolley of mass $2\ \text{kg}$ on a smooth level floor so that it accelerates at $3\ \text{m s}^{-2}$?
  1. A $6\ \text{N}$
  2. B $0.67\ \text{N}$
  3. C $1.5\ \text{N}$
  4. D $5\ \text{N}$
Show answer and explanation

Correct answer: A - $6\ \text{N}$

The force needed is mass multiplied by acceleration, $2 \times 3 = 6\ \text{N}$. Dividing the acceleration by the mass gives $1.5$ and dividing the mass by the acceleration gives $0.67$, but both quantities must be multiplied. Adding them gives $5$, which is not a force at all.

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