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Karnataka PUC I Kinetic Theory & Oscillations — practice questions — page 2

Explore 50 free Kinetic Theory & Oscillations questions in Karnataka PUC I 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 31–50 of 50.

The ratio of average KE of a monatomic gas to that of a rigid diatomic gas, at the **same T**, is:Read the answer and worked solution →Velocity of sound in an ideal gas is $v_s = \sqrt{\gamma RT/M_0}$. Compared to rms speed, $v_s$:Read the answer and worked solution →The rms speed of helium atom at 300 K is approximately (M_He = 4 g/mol):Read the answer and worked solution →The internal energy of 2 moles of nitrogen gas (rigid diatomic) at 300 K is approximately ($R = 8.314$):Read the answer and worked solution →If the mean free path of N₂ at 1 atm is ~80 nm, what is it at 0.01 atm (same T)?Read the answer and worked solution →The number of moles of oxygen ($O_2$) gas in a vessel of volume 1 L at STP (273.15 K, 1.013 × 10⁵ Pa) is approximately:Read the answer and worked solution →The time period of a simple pendulum of length $L$ is:Read the answer and worked solution →Time period of a spring-mass system (spring constant $k$, mass $m$) is:Read the answer and worked solution →At the **mean (equilibrium) position** of SHM, which is true?Read the answer and worked solution →Total mechanical energy of a particle in SHM (mass $m$, amplitude $A$, angular frequency $\omega$) is:Read the answer and worked solution →If displacement of a particle in SHM is $x = A\sin(\omega t)$, velocity at $x = A/2$ is:Read the answer and worked solution →In SHM, when the displacement is half the amplitude (x = A/2), the ratio of KE to PE is:Read the answer and worked solution →A simple pendulum of period $T$ on Earth is taken to the Moon where $g_{moon} = g/6$. Its new period is:Read the answer and worked solution →The phase difference between displacement $x$ and velocity $v$ in SHM is:Read the answer and worked solution →A spring of force constant $k$ is cut into two equal halves. The force constant of each half is:Read the answer and worked solution →Two springs of constants $k_1$ and $k_2$ connected in **series** have effective spring constant:Read the answer and worked solution →If $x_1 = A\sin(\omega t)$ and $x_2 = A\sin(\omega t + \pi/3)$, the resultant amplitude of $x_1 + x_2$ is: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 →NEET · Physics · Kinetic Theory — SortRead the answer and worked solution →NEET · Physics · Oscillation Period — Gap FillRead the answer and worked solution →

Worked practice questions

The ratio of average KE of a monatomic gas to that of a rigid diatomic gas, at the **same T**, is:

  1. 3:5 (monatomic 3 DOF, diatomic 5 DOF, all × ½ k_BT)
  2. 1:1
  3. 5:3
  4. Cannot be determined
Show answer and solution

Correct answer: A. 3:5 (monatomic 3 DOF, diatomic 5 DOF, all × ½ k_BT)

Average energy per molecule = (DOF/2) k_B T. Monatomic: (3/2) k_B T. Diatomic rigid: (5/2) k_B T. Ratio = 3:5.

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Velocity of sound in an ideal gas is $v_s = \sqrt{\gamma RT/M_0}$. Compared to rms speed, $v_s$:

  1. Equals $v_{rms}$ always
  2. Is smaller than $v_{rms}$ (since $\gamma \le 5/3 < 3$)
  3. Is larger than $v_{rms}$
  4. Can be zero
Show answer and solution

Correct answer: B. Is smaller than $v_{rms}$ (since $\gamma \le 5/3 < 3$)

$v_s/v_{rms} = \sqrt{\gamma/3}$. Since $\gamma \le 5/3 < 3$, $v_s < v_{rms}$ always. (Sound waves can't propagate faster than the molecules they ride on.) For monatomic gas, ratio = $\sqrt{5/9} \approx 0.745$.

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The rms speed of helium atom at 300 K is approximately (M_He = 4 g/mol):

  1. ~ 137 m/s
  2. ~ 1368 m/s
  3. ~ 5000 m/s
  4. ~ 14 m/s
Show answer and solution

Correct answer: B. ~ 1368 m/s

$v_{rms} = \sqrt{3RT/M_0} = \sqrt{3 \cdot 8.314 \cdot 300/0.004} = \sqrt{1.87 \times 10^6} \approx 1368$ m/s. (Helium escapes Earth's atmosphere over time because rms speed exceeds escape velocity for many atoms at higher altitudes.)

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