Q. No.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: Β Spring mass system |
Β 60%
Level 2: 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: Β Spring mass system |
Β 78%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses \(1~\text{kg}\) and \(0.2~\text{kg}\) with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is:
1. \(30\)
2. \(27\)
3. \(20\)
4. \(5\)
1. \(30\)
2. \(27\)
3. \(20\)
4. \(5\)
Subtopic: Β Spring mass system |
Β 64%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Two blocks of masses \(m\) and \(M, (M>m), \) are placed on a frictionless table as shown in figure. A massless spring with spring constant \(k\) is attached with the lower block. If the system is slightly displaced and released, then (\(\mu =\) coefficient of friction between the two blocks)
Choose the correct answer from the options given below:
| \(\mathrm{A.}\) | The time period of small oscillation of the two blocks is \(T=2 \pi \sqrt{\dfrac{({m}+{M})}{{k}}}\) |
| \(\mathrm{B.}\) | The acceleration of the blocks is \(a=-\dfrac{k x}{M+m},(x=\)displacement of the blocks from the mean position) |
| \(\mathrm{C.}\) | The magnitude of the frictional force on the upper block is \(\dfrac{m \mu|x|}{M+m}\) |
| \(\mathrm{D.}\) | The maximum amplitude of the upper block, if it does not slip, is \(\dfrac{\mu(M+m) g}{k}\) |
| \(\mathrm{E.}\) | Maximum frictional force can be \(\mu(M+m)g\) |
| 1. | \(\mathrm{A, B, C}~\text{Only}\) | 2. | \(\mathrm{A, B, D}~\text{Only}\) |
| 3. | \(\mathrm{C, D, E}~\text{Only}\) | 4. | \(\mathrm{B, C, D}~\text{Only}\) |
Subtopic: Β Spring mass system |
Β 70%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Two bodies \(A\) and \(B\) of equal mass are suspended from two massless springs of spring constant \(k_1\) and \(k_2\), respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of \(A\) to the maximum velocity of \(B\) is:
1. \(\dfrac{k_1}{k_2}\)
2. \(\sqrt{\dfrac{k_1}{k_2}} \)
3. \(\sqrt{\dfrac{{k}_2}{{k}_1}} \)
4. \(\dfrac{k_2}{k_1} \)
1. \(\dfrac{k_1}{k_2}\)
2. \(\sqrt{\dfrac{k_1}{k_2}} \)
3. \(\sqrt{\dfrac{{k}_2}{{k}_1}} \)
4. \(\dfrac{k_2}{k_1} \)
Subtopic: Β Spring mass system |
Β 70%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A block of mass \(m\) is connected with a spring, and the time period of its oscillation is \({T.}\) If the mass is increased to \({9m}\) while keeping the same spring, the new time period of oscillation will be:
1. \(3T\)
2. \(\dfrac{3}{2}T\)
3. \({5}T\)
4. \(\dfrac{T}{5}\)
1. \(3T\)
2. \(\dfrac{3}{2}T\)
3. \({5}T\)
4. \(\dfrac{T}{5}\)
Subtopic: Β Spring mass system |
Β 88%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
For the oscillations exhibited by the spring-block system, on a smooth surface (along the springs), the time period is:
| 1. | \(\begin{aligned} {2}\mathit{\pi}\sqrt{\dfrac{{m}\left({{k}_{1}{+}{k}_{2}}\right)}{{k}_{1}{k}_{2}}} & \end{aligned}\) | 2. | \(\begin{aligned}2\pi\sqrt{{{m\left({k_{1}+k_{2}}\right)}\over{2k_{1}k_{2}}}} &\end{aligned}\) |
| 3. | \(\begin{aligned} 2\pi\sqrt{{{m}\over{k_{1}+k_{2}}}} & \end{aligned}\) | 4. | \(\begin{aligned} \pi\sqrt{{{m}\over{k_{1}+k_{2}}}} & \end{aligned}\) |
Subtopic: Β Spring mass system |
Β 71%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A block of mass \(2\) kg is attached to two identical springs, each with a force constant of \(20\) N/m, as shown in the figure. The time period of the oscillation of the block is:
| 1. | \(2\pi \sqrt{\dfrac{1}{20}}\) s | 2. | \(\pi \sqrt{\dfrac{1}{20}}\) s |
| 3. | \(2\pi \sqrt{\dfrac{1}{10}}\) s | 4. | \(\pi \sqrt{\dfrac{1}{10}}\) s |
Subtopic: Β Spring mass system |
Β 72%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A block of mass \(m\) is connected to two identical springs of force constant \(K\) as shown. The frequency of the block is:
1. \({2}\mathit{\pi}\sqrt{\left[{\frac{2m}{K}}\right]}\)
2. \(\frac{1}{{2}\mathit{\pi}}\sqrt{\left[{\frac{K}{m}}\right]}\)
3. \({2}\mathit{\pi}\sqrt{\left[{\frac{m}{2K}}\right]}\)
4. \(\frac{1}{{2}\mathit{\pi}}\sqrt{\left[{\frac{2K}{m}}\right]}\)
1. \({2}\mathit{\pi}\sqrt{\left[{\frac{2m}{K}}\right]}\)
2. \(\frac{1}{{2}\mathit{\pi}}\sqrt{\left[{\frac{K}{m}}\right]}\)
3. \({2}\mathit{\pi}\sqrt{\left[{\frac{m}{2K}}\right]}\)
4. \(\frac{1}{{2}\mathit{\pi}}\sqrt{\left[{\frac{2K}{m}}\right]}\)
Subtopic: Β Spring mass system |
Β 76%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
In the shown mass-spring system, when it is set into oscillations along the spring, it has angular frequency \(\omega_1\) if \(m=1\) kg and \(\omega_2\) if \(m=2\) kg. Then the value of \(\dfrac{\omega_1}{\omega_2}\) is equal to:
1. \(1\)
2. \(\sqrt{2}\)
3. \(\frac{1}{\sqrt{2}}\)
4. \(2\)
1. \(1\)
2. \(\sqrt{2}\)
3. \(\frac{1}{\sqrt{2}}\)
4. \(2\)
Subtopic: Β Spring mass system |
Β 82%
Level 1: 80%+
Please attempt this question first.
Hints
Please attempt this question first.
Β© 2026 GoodEd Technologies Pvt. Ltd.