Gravitation, oscillations and waves are linked by a few compact formulas that JEE tests in many forms. This set covers escape and orbital velocity, Kepler's third law, SHM energy, springs and pendulums, wave speed on strings, organ pipes, the Doppler effect and beats. Take g = 10 m/s² and the speed of sound as 340 m/s unless stated otherwise.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Variation of g with height and density
- Escape velocity, orbital velocity and Kepler's laws
- SHM: displacement, velocity, acceleration and energy
- Spring-mass systems and the simple pendulum
- Wave speed on a string and organ pipes
- Doppler effect and beats
JEE Physics MCQs with answers and explanations
Q1. How is the escape velocity from the surface of a planet related to the orbital velocity of a satellite just above its surface?
a) v_e = v_o
b) v_e = v_o/√2
c) v_e = 2v_o
d) v_e = √2 v_o
Q2. What is the acceleration due to gravity at a height equal to the Earth's radius R above its surface?
a) g/√2
b) g/4
c) g/2
d) g/8
Q3. The orbital radius of a planet around the Sun is made 4 times larger. Its time period becomes:
a) 4 times
b) 16 times
c) 8 times
d) 2 times
Q4. A planet has the same mean density as the Earth but twice its radius. The acceleration due to gravity on its surface is:
a) 4g
b) g
c) 2g
d) g/2
Q5. Taking g = 10 m/s² and R = 6,400 km, what is the escape velocity from the Earth's surface?
a) 8.0 km/s
b) 5.7 km/s
c) 16.0 km/s
d) 11.3 km/s
Q6. A particle moves in SHM as x = 0.1 sin(10t) m. What is its maximum speed?
a) 100 m/s
b) 0.1 m/s
c) 10 m/s
d) 1 m/s
Q7. A 1 kg mass hangs from a spring of spring constant 100 N/m. What is the period of its vertical oscillations?
a) π/10 s
b) π/5 s
c) π s
d) 2π s
Q8. The length of a simple pendulum is made 4 times larger. Its time period becomes:
a) Half
b) 2 times
c) 4 times
d) Unchanged
Q9. In SHM of amplitude A, what fraction of the total energy is kinetic when the displacement is A/2?
a) 3/4
b) 1/4
c) 1
d) 1/2
Q10. Two identical springs of constant k are joined in series and a mass m hangs from them. Compared with one spring alone, the period becomes:
a) 1/√2 times
b) √2 times
c) Unchanged
d) 2 times
Q11. A string has tension 100 N and linear mass density 0.01 kg/m. What is the speed of transverse waves on it?
a) 100 m/s
b) 10,000 m/s
c) 10 m/s
d) 1,000 m/s
Q12. A pipe closed at one end is 85 cm long. What is its fundamental frequency? (speed of sound 340 m/s, ignore end correction)
a) 100 Hz
b) 200 Hz
c) 400 Hz
d) 50 Hz
Q13. Which harmonics are present in a pipe closed at one end?
a) Only even harmonics
b) Only the fundamental
c) All harmonics
d) Only odd harmonics
Q14. A source of 500 Hz moves towards a stationary listener at 34 m/s. What frequency does the listener hear? (speed of sound 340 m/s)
a) 500 Hz
b) 450 Hz
c) 550 Hz
d) 555.6 Hz
Q15. Two tuning forks of 256 Hz and 260 Hz are sounded together. How many beats are heard per second?
a) 258
b) 2
c) 4
d) 8
Quick revision notes
- g at height h: GM/(R + h)²; g ∝ ρR at fixed density.
- v_o = √(GM/R), v_e = √(2GM/R) = √(2gR); T² ∝ r³.
- SHM: v_max = Aω, a_max = Aω²; KE = ½k(A² − x²).
- Spring T = 2π√(m/k); pendulum T = 2π√(L/g); series k/2, parallel 2k.
- v = √(T/μ); closed pipe f = v/4L (odd harmonics); Doppler f' = f(v ± v_o)/(v ∓ v_s); beats = |f₁ − f₂|.
Frequently asked questions
Are these JEE previous year questions?
No. They are original practice questions at the JEE Main level.
How do I remember the signs in the Doppler formula?
Motion that brings source and listener closer must raise the frequency. Pick the sign in the numerator and denominator that makes this happen.
Does the period of a pendulum depend on the mass of the bob?
No. For small oscillations it depends only on length and g. A spring-mass period depends on mass but not on g.
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