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JEE Main Kinetic Theory & Oscillations — practice questions

Explore 33 free Kinetic Theory & Oscillations questions in JEE Main Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Kinetic Theory & Oscillations questions and exercises with answers

Showing questions 1–30 of 33.

The time period of a simple pendulum of length $L$ in a gravitational field $g$ is:Read the answer and worked solution →A particle in SHM has amplitude $A$ and angular frequency $\omega$. Its maximum speed is:Read the answer and worked solution →The time period of a spring-mass system with mass $m$ and spring constant $k$ is:Read the answer and worked solution →The total mechanical energy of a particle of mass $m$ in SHM with amplitude $A$ and angular frequency $\omega$ is:Read the answer and worked solution →The root-mean-square (rms) speed of gas molecules is given by:Read the answer and worked solution →The mean translational kinetic energy of one molecule of an ideal gas at temperature $T$ is:Read the answer and worked solution →If the absolute temperature of an ideal gas is doubled, the rms speed of its molecules:Read the answer and worked solution →The mean free path $\lambda$ of a gas molecule of diameter $d$ at number density $n$ is approximately:Read the answer and worked solution →For an ideal gas, the relationship between $C_p$ and $C_v$ is (Mayer's relation):Read the answer and worked solution →A diatomic ideal gas has $C_v = \tfrac{5}{2}R$. Its $C_p$ and ratio $\gamma$ are:Read the answer and worked solution →Motion in which an object moves to and fro about a mean position is called:Read the answer and worked solution →The smallest interval of time after which the motion repeats is called its:Read the answer and worked solution →The number of repetitions per unit time is given by the reciprocal of the:Read the answer and worked solution →The unit of frequency is named after which discoverer of radio waves?Read the answer and worked solution →Which is described as the simplest form of oscillatory motion?Read the answer and worked solution →In simple harmonic motion, the force is always directed towards the:Read the answer and worked solution →The force that always points back towards the mean position is called the:Read the answer and worked solution →Which statement about oscillatory and periodic motion is correct?Read the answer and worked solution →Simple harmonic motion is shown to be the projection on a diameter of which motion?Read the answer and worked solution →In simple harmonic motion, which quantity does the symbol A stand for?Read the answer and worked solution →In the standard symbols for simple harmonic motion, phi stands for the phase:Read the answer and worked solution →Both kinetic and potential energy of a particle in simple harmonic motion vary between zero and their:Read the answer and worked solution →Describing periodic motion needs period, frequency, amplitude, phase and:Read the answer and worked solution →The total mechanical energy of a harmonic oscillator is independent of:Read the answer and worked solution →Why is the total mechanical energy of a harmonic oscillator constant?Read the answer and worked solution →Oscillations kept going by an external periodic agency are described as:Read the answer and worked solution →One hertz is defined as how many oscillations per second?Read the answer and worked solution →Is the frequency of an oscillation necessarily a whole number?Read the answer and worked solution →Periodic and oscillatoryRead the answer and worked solution →Name the symbolRead the answer and worked solution →

Worked practice questions

The time period of a simple pendulum of length $L$ in a gravitational field $g$ is:

  1. $T = 2\pi \sqrt{\dfrac{L}{g}}$
  2. $T = 2\pi \sqrt{\dfrac{g}{L}}$
  3. $T = 2\pi L g$
  4. $T = \sqrt{\dfrac{L}{g}}$
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Correct answer: A. $T = 2\pi \sqrt{\dfrac{L}{g}}$

For small oscillations the pendulum's equation of motion reduces to SHM with $\omega = \sqrt{g/L}$. So period $T = 2\pi/\omega = 2\pi\sqrt{L/g}$. Independent of the mass of the bob (a key contrast with the spring-mass system, where $T \propto \sqrt{m}$). Note: only valid for small-amplitude swings. At larger amplitudes the small-angle approximation fails and the period depends slightly on amplitude.

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A particle in SHM has amplitude $A$ and angular frequency $\omega$. Its maximum speed is:

  1. $A\omega$
  2. $A\omega^2$
  3. $A/\omega$
  4. $\omega/A$
Show answer and solution

Correct answer: A. $A\omega$

Position $x(t) = A \sin(\omega t + \phi)$. Velocity is its time derivative: $v(t) = A\omega \cos(\omega t + \phi)$. Maximum value is $v_{\max} = A\omega$, achieved when the particle passes through the mean position ($x = 0$). Maximum acceleration is at the extremes: $a_{\max} = A\omega^2$ (option B is the acceleration max, the common trap).

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The time period of a spring-mass system with mass $m$ and spring constant $k$ is:

  1. $T = 2\pi \sqrt{\dfrac{k}{m}}$
  2. $T = 2\pi \sqrt{\dfrac{m}{k}}$
  3. $T = 2\pi k m$
  4. $T = 2\pi (k + m)$
Show answer and solution

Correct answer: B. $T = 2\pi \sqrt{\dfrac{m}{k}}$

Spring-mass system: Newton's second law gives $m\ddot x = -kx$, hence $\omega = \sqrt{k/m}$. Period: $T = \dfrac{2\pi}{\omega} = 2\pi\sqrt{m/k}$. A stiffer spring (larger $k$) gives a shorter period. A heavier mass gives a longer period. Option A inverts the ratio, the classic trap.

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