Select Chapter Topics:
Q. No.A uniform disc of radius \(R\) and mass \(M\) is free to oscillate about the axis \(A\) as shown in the figure. For small oscillations the time period is:
(\(g\) is acceleration due to gravity)
1. \(2 \pi \sqrt{\dfrac{5 R}{4 g}}~\)
2. \(2 \pi \sqrt{\dfrac{2 R}{3 g}}~\)
3. \(2 \pi \sqrt{\dfrac{3 R}{2 g}}~\)
4. \(2 \pi \sqrt{\dfrac{3 R}{g}}~\)
(\(g\) is acceleration due to gravity)
1. \(2 \pi \sqrt{\dfrac{5 R}{4 g}}~\)
2. \(2 \pi \sqrt{\dfrac{2 R}{3 g}}~\)
3. \(2 \pi \sqrt{\dfrac{3 R}{2 g}}~\)
4. \(2 \pi \sqrt{\dfrac{3 R}{g}}~\)
Subtopic: Simple Harmonic Motion |
Level 4: Below 35%
Please attempt this question first.
Hints
Please attempt this question first.
A spring stretches by \(2~\text{mm}\) when it is loaded with a mass of \(200~\text{g}.\) From equilibrium position the mass is further pulled down by \(2~\text{mm}\) and released. The frequency associated with the system and maxmimum energy in the spring are
( Take\(g =10~\text{m/s}^{2}\)
1. \(\dfrac{5 \sqrt{50}}{\pi}~\text{and}~8 \times 10^{-3} \)
2. \( \dfrac{5 \sqrt{50}}{\pi}~\text{and}~8 \)
3. \(10 \sqrt{50}~ \text{and}~2 \times 10^{-3} \)
4. \(\dfrac{5 \sqrt{50}}{\pi} ~\text{and}~16 \times 10^{-3}\)
( Take
1. \(\dfrac{5 \sqrt{50}}{\pi}~\text{and}~8 \times 10^{-3} \)
2. \( \dfrac{5 \sqrt{50}}{\pi}~\text{and}~8 \)
3. \(10 \sqrt{50}~ \text{and}~2 \times 10^{-3} \)
4. \(\dfrac{5 \sqrt{50}}{\pi} ~\text{and}~16 \times 10^{-3}\)
Subtopic: Spring mass system |
63%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A particle is executing simple harmonic motion. Its amplitude is \(A\) and time period is \(5~\text{s}\). The time required by it to move from \(x=A \text { to } x=\dfrac{A}{\sqrt{2}}\) is: (in s)
1. \(1/4\)
2. \(5/4\)
3. \(5/8\)
4. \(3/8\)
1. \(1/4\)
2. \(5/4\)
3. \(5/8\)
4. \(3/8\)
Subtopic: Angular SHM |
91%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
Match List-I with List-II.
Choose the correct answer from the options given below:
1. \(\mathrm{A\text-III, B\text-I, C\text-IV, D\text-II }\)
2. \(\mathrm{A\text-II, B\text-I, C\text-III, D\text-IV }\)
3. \(\mathrm{A\text-III, B\text-II, C\text-IV, D\text-I}\)
4. \(\mathrm{A\text-II, B\text-I, C\text-IV, D\text-III }\)
| List-I | List-II | ||
| \(\mathrm{(A)}\) | \(\sin ^2 \omega t\) | \(\mathrm{(I)}\) | Periodic with time period \(T=\dfrac{\pi}{\omega}\) but not simple harmonic motion (\(\mathrm{SHM}\)) |
| \(\mathrm{(B)}\) | \(\sin ^3(2 \omega t)\) | \(\mathrm{(II)}\) | Periodic with time period \(T=\dfrac{2\pi}{\omega}\) but Not \(\mathrm{SHM}\) |
| \(\mathrm{(C)}\) | \(\sin (\omega t)+\cos (\pi \omega t)\) | \(\mathrm{(III)}\) | Periodic with time period \(T=\dfrac{\pi}{\omega}\) and \(\mathrm{SHM}\) |
| \(\mathrm{(D)}\) | \(\cos \omega t+\cos 2 \omega t\) | \(\mathrm{(IV)}\) | Non-periodic |
1. \(\mathrm{A\text-III, B\text-I, C\text-IV, D\text-II }\)
2. \(\mathrm{A\text-II, B\text-I, C\text-III, D\text-IV }\)
3. \(\mathrm{A\text-III, B\text-II, C\text-IV, D\text-I}\)
4. \(\mathrm{A\text-II, B\text-I, C\text-IV, D\text-III }\)
Subtopic: Simple Harmonic Motion |
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
The frequency of oscillation of mass \(m\) suspended by a spring is \(\nu_1\). If the length of spring is cut to half, the same mass oscillates with frequency \(\nu_2\). The value of \(\nu_2 / \nu_1\) is:
1. \(1\)
2. \(2\)
3. \(\sqrt2\)
4. \(\sqrt3\)
1. \(1\)
2. \(2\)
3. \(\sqrt2\)
4. \(\sqrt3\)
Subtopic: Spring mass system |
75%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
The velocity of a particle executing simple harmonic motion along \(x\text{-axis}\) is described as \(v^2=50-x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7} ~\text{s}\), the value of \(x\) is:
1. \(44\)
2. \(50\)
3. \(60\)
4. \(80\)
1. \(44\)
2. \(50\)
3. \(60\)
4. \(80\)
Subtopic: Simple Harmonic Motion |
82%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
The kinetic energy of a particle executing simple harmonic motion varies periodically with an angular frequency of \(176~\text{rad/s}.\) The frequency (in Hz) of the oscillator is: \(\left ( \pi =22/7 \right )\)
1. \(14\)
2. \(88\)
3. \(28\)
4. \(176\)
1. \(14\)
2. \(88\)
3. \(28\)
4. \(176\)
Subtopic: Energy of SHM |
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
Using a simple pendulum experiment \(g\) is determined by measuring its time period \(T\). Which of the following plots represent the correct relation between the pendulum length \(L\) and time period \(T\)?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Angular SHM |
72%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A simple pendulum of string length \(30\) cm performs \(20\) oscillations in \(10~\text{s}\). The length of the string required for the pendulum to perform \(40\) oscillations in the same time duration is: (in cm) [Assume that the mass of the pendulum remains same.]
1. \(120\)
2. \(0.75\)
3. \(7.5\)
4. \(15\)
1. \(120\)
2. \(0.75\)
3. \(7.5\)
4. \(15\)
Subtopic: Angular SHM |
81%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
A cylindrical block of mass \(M\) and area of cross section \(A\) is floating in a liquid of density \(\rho\) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is:
1. \(2 \pi \sqrt{\dfrac{M}{\rho A g}}\)
2. \(\pi \sqrt{\dfrac{2{M}}{\rho {Ag}}}\)
3. \(\pi \sqrt{\dfrac{\rho {A}}{{Mg}}}\)
4. \(2\pi \sqrt{\dfrac{\rho {A}}{{Mg}}}\)
1. \(2 \pi \sqrt{\dfrac{M}{\rho A g}}\)
2. \(\pi \sqrt{\dfrac{2{M}}{\rho {Ag}}}\)
3. \(\pi \sqrt{\dfrac{\rho {A}}{{Mg}}}\)
4. \(2\pi \sqrt{\dfrac{\rho {A}}{{Mg}}}\)
Subtopic: Simple Harmonic Motion |
91%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
Select Chapter Topics:
© 2026 GoodEd Technologies Pvt. Ltd.