CSS Physics chapter 1: Mathematical methods and mechanics MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

80 exam-style questions on Mathematical methods and mechanics, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

80 questions · 5 topics · 10 per test

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What chapter 1 covers

Ten Mathematical methods and mechanics questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A pipe closed at one end has a fundamental frequency of 100 Hz. Which of these frequencies can also be sounded as a resonance of this pipe?

  1. A
    300 Hz
  2. B
    200 Hz
  3. C
    400 Hz
  4. D
    150 Hz
Show answer

Answer: A. A closed pipe supports only odd harmonics: 100, 300, 500 Hz and so on, because it needs a node at the closed end and an antinode at the open end.

2. A satellite of mass m moves in a circular orbit of radius r about a planet of mass M. Its total mechanical energy is

  1. A
    +GMm/(2r)
  2. B
    −GMm/r
  3. C
    −GMm/(2r)
  4. D
    −GMm/(4r)
Show answer

Answer: C. KE = GMm/(2r) and PE = −GMm/r, so the total is −GMm/(2r). The negative sign shows that the satellite is bound.

3. A body's speed is doubled and its mass is halved. Its kinetic energy

  1. A
    stays the same
  2. B
    quadruples
  3. C
    doubles
  4. D
    is halved
Show answer

Answer: C. KE = ½mv2. The new value is ½(m/2)(2v)2 = ½ × (m/2) × 4v2 = 2 × (½mv2).

4. A planet has eight times the mass of the Earth and twice its radius. The acceleration due to gravity at its surface is

  1. A
    4g
  2. B
    2g
  3. C
    g/2
  4. D
    8g
Show answer

Answer: B. g = GM/R2, so the ratio to Earth's value is 8/22 = 2.

5. A source of frequency 320 Hz moves directly towards a stationary observer at 20 m s−1. The speed of sound is 340 m s−1. The frequency heard by the observer is

  1. A
    320 Hz
  2. B
    360 Hz
  3. C
    340 Hz
  4. D
    300 Hz
Show answer

Answer: C. f′ = f v/(v − vs) = 320 × 340/320 = 340 Hz. Using 340 + 20 in the denominator would apply to a receding source.

6. A force F = (3i − 2j) N moves its point of application through a displacement d = (4i + 3j) m. The work done is

  1. A
    18 J
  2. B
    12 J
  3. C
    9 J
  4. D
    6 J
Show answer

Answer: D. Work is the dot product: W = F·d = (3)(4) + (−2)(3) = 12 − 6 = 6 J. 18 J comes from ignoring the sign of the j-component, and 12 J keeps only the x-terms.

7. A 2 kg mass moves in a horizontal circle of radius 0.5 m at a constant speed of 4 m s−1. The magnitude of the centripetal force on it is

  1. A
    64 N
  2. B
    32 N
  3. C
    16 N
  4. D
    128 N
Show answer

Answer: A. F = mv2/r = 2 × 16 / 0.5 = 64 N, directed towards the centre.

8. A 2 kg trolley moving at 6 m s−1 collides with a stationary 4 kg trolley and the two stick together. Their common speed after the collision is

  1. A
    3 m s−1
  2. B
    1.5 m s−1
  3. C
    4 m s−1
  4. D
    2 m s−1
Show answer

Answer: D. Momentum is conserved: 2 × 6 = (2 + 4)v, so v = 12/6 = 2 m s−1. The speed 3 m s−1 would be the result if the mass of 4 kg were ignored.

9. A constant force of 50 N acts for 0.2 s on a 0.5 kg ball initially at rest. The speed of the ball after the force stops is

  1. A
    20 m s−1
  2. B
    10 m s−1
  3. C
    5 m s−1
  4. D
    40 m s−1
Show answer

Answer: A. Impulse = Ft = 50 × 0.2 = 10 N s equals the change of momentum, so v = 10 / 0.5 = 20 m s−1.

10. A book rests on a horizontal table. The Earth pulls the book downwards with its weight. By Newton's third law, the reaction to this weight is the force exerted by

  1. A
    the table on the book
  2. B
    the table on the Earth
  3. C
    the Earth on the table
  4. D
    the book on the Earth
Show answer

Answer: D. A reaction pair acts on two different bodies, is of the same type and is equal and opposite: Earth pulls book, so book pulls Earth. The normal force from the table balances the weight but is not its third-law partner.

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Mathematical methods and mechanics: questions students ask

How many Mathematical methods and mechanics MCQs are there?

80, each with the answer and a short explanation, across 5 topics: Vectors and vector analysis, Kinematics, Newton's laws, work, energy and momentum, Rotational motion and gravitation, Oscillations and waves. Every chapter test draws ten of them, so you can take it many times.

Is the CSS Physics chapter 1 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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