Spring and Its Combination, Two Body Spring System
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Oscillations

140621 One end of a massless spring of spring constant $\mathrm{k}$ and natural length $l_{0}$ is fixed while the other end is connected to a small object of mass $\mathbf{m}$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be:

1 $\frac{\mathrm{k}-\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
2 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}+\mathrm{m} \omega^{2}}$
3 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}-\mathrm{m} \omega^{2}}$
4 $\frac{\mathrm{k}+\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
JEE Main-27.06.2022
Oscillations

140622 As per the given figure, two blocks each of mass $250 \mathrm{~g}$ are connected to a spring of spring constant $2 \mathrm{Nm}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is:

1 $\frac{\mathrm{V}}{2 \sqrt{2}}$
2 $\frac{\mathrm{V}}{2}$
3 $\frac{\mathrm{v}}{4}$
4 $\frac{\mathrm{v}}{\sqrt{2}}$
JEE Main-26.07.2022
Oscillations

140623 In figure (A), mass ' $2 \mathrm{~m}$ ' is fixed on mass ' $\mathrm{m}$ ' which is attached to two springs of spring constant $k$. In figure (B) mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in (A) and (B) are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to (A) and (B) respectively follow the relation.

1 $\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}$
2 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}}$
3 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\sqrt{2}}{3}$
JEE Main-25.07.2022
Oscillations

140624 The restoring force of a spring with a block attached to the free end of the spring is represented by:

1 a
2 b
3 d
4 d
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Oscillations

140621 One end of a massless spring of spring constant $\mathrm{k}$ and natural length $l_{0}$ is fixed while the other end is connected to a small object of mass $\mathbf{m}$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be:

1 $\frac{\mathrm{k}-\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
2 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}+\mathrm{m} \omega^{2}}$
3 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}-\mathrm{m} \omega^{2}}$
4 $\frac{\mathrm{k}+\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
JEE Main-27.06.2022
Oscillations

140622 As per the given figure, two blocks each of mass $250 \mathrm{~g}$ are connected to a spring of spring constant $2 \mathrm{Nm}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is:

1 $\frac{\mathrm{V}}{2 \sqrt{2}}$
2 $\frac{\mathrm{V}}{2}$
3 $\frac{\mathrm{v}}{4}$
4 $\frac{\mathrm{v}}{\sqrt{2}}$
JEE Main-26.07.2022
Oscillations

140623 In figure (A), mass ' $2 \mathrm{~m}$ ' is fixed on mass ' $\mathrm{m}$ ' which is attached to two springs of spring constant $k$. In figure (B) mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in (A) and (B) are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to (A) and (B) respectively follow the relation.

1 $\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}$
2 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}}$
3 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\sqrt{2}}{3}$
JEE Main-25.07.2022
Oscillations

140624 The restoring force of a spring with a block attached to the free end of the spring is represented by:

1 a
2 b
3 d
4 d
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Oscillations

140621 One end of a massless spring of spring constant $\mathrm{k}$ and natural length $l_{0}$ is fixed while the other end is connected to a small object of mass $\mathbf{m}$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be:

1 $\frac{\mathrm{k}-\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
2 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}+\mathrm{m} \omega^{2}}$
3 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}-\mathrm{m} \omega^{2}}$
4 $\frac{\mathrm{k}+\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
JEE Main-27.06.2022
Oscillations

140622 As per the given figure, two blocks each of mass $250 \mathrm{~g}$ are connected to a spring of spring constant $2 \mathrm{Nm}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is:

1 $\frac{\mathrm{V}}{2 \sqrt{2}}$
2 $\frac{\mathrm{V}}{2}$
3 $\frac{\mathrm{v}}{4}$
4 $\frac{\mathrm{v}}{\sqrt{2}}$
JEE Main-26.07.2022
Oscillations

140623 In figure (A), mass ' $2 \mathrm{~m}$ ' is fixed on mass ' $\mathrm{m}$ ' which is attached to two springs of spring constant $k$. In figure (B) mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in (A) and (B) are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to (A) and (B) respectively follow the relation.

1 $\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}$
2 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}}$
3 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\sqrt{2}}{3}$
JEE Main-25.07.2022
Oscillations

140624 The restoring force of a spring with a block attached to the free end of the spring is represented by:

1 a
2 b
3 d
4 d
NEET 2022
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Oscillations

140621 One end of a massless spring of spring constant $\mathrm{k}$ and natural length $l_{0}$ is fixed while the other end is connected to a small object of mass $\mathbf{m}$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be:

1 $\frac{\mathrm{k}-\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
2 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}+\mathrm{m} \omega^{2}}$
3 $\frac{\mathrm{m} \omega^{2} l_{0}}{\mathrm{k}-\mathrm{m} \omega^{2}}$
4 $\frac{\mathrm{k}+\mathrm{m} \omega^{2} l_{0}}{\mathrm{~m} \omega^{2}}$
JEE Main-27.06.2022
Oscillations

140622 As per the given figure, two blocks each of mass $250 \mathrm{~g}$ are connected to a spring of spring constant $2 \mathrm{Nm}^{-1}$. If both are given velocity $v$ in opposite directions, then maximum elongation of the spring is:

1 $\frac{\mathrm{V}}{2 \sqrt{2}}$
2 $\frac{\mathrm{V}}{2}$
3 $\frac{\mathrm{v}}{4}$
4 $\frac{\mathrm{v}}{\sqrt{2}}$
JEE Main-26.07.2022
Oscillations

140623 In figure (A), mass ' $2 \mathrm{~m}$ ' is fixed on mass ' $\mathrm{m}$ ' which is attached to two springs of spring constant $k$. In figure (B) mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2 k$ '. If mass ' $m$ ' in (A) and (B) are displaced by distance ' $x$ ' horizontally and then released, then time period $T_{1}$ and $T_{2}$ corresponding to (A) and (B) respectively follow the relation.

1 $\frac{T_{1}}{T_{2}}=\frac{3}{\sqrt{2}}$
2 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{3}{2}}$
3 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\sqrt{\frac{2}{3}}$
4 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\frac{\sqrt{2}}{3}$
JEE Main-25.07.2022
Oscillations

140624 The restoring force of a spring with a block attached to the free end of the spring is represented by:

1 a
2 b
3 d
4 d
NEET 2022
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