Some Systems Executing Simple Harmonic Motion
PHXI14:OSCILLATIONS

364403 A horizontal rod of mass \(m\) and length \(L\) is pivoted at one end. The rod's other end is supported by a spring of force constant \(k\). The rod is displaced by a small angle \(\theta\) from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is
supporting img

1 \(\sqrt{\dfrac{k}{3 m}}\)
2 \(\sqrt{\dfrac{3 k}{m}}\)
3 \(\sqrt{\dfrac{k}{m}}\)
4 \(\sqrt{\dfrac{3 k}{m}+\dfrac{3 g}{2 L}}\)
PHXI14:OSCILLATIONS

364404 Assertion :
The spring constant of a spring is \(k\). When it is divided into \(n\) equal parts, then spring constant of one piece is \(k{\rm{/}}n.\)
Reason :
The spring constant depends on material used for the spring.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI14:OSCILLATIONS

364405 Two bodies \(A\) and \(B\) of equal mass are suspended from two separate massles springs of force constant \(k_{1}\) and \(k_{2}\) respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body \(A\) to that of body \(B\) is

1 \(\sqrt{\dfrac{k_{2}}{k_{1}}}\)
2 \(\dfrac{k_{2}}{k_{1}}\)
3 \(\dfrac{k_{1}}{k_{2}}\)
4 \(\sqrt{\dfrac{k_{1}}{k_{2}}}\)
PHXI14:OSCILLATIONS

364406 A block \(A\) of mass \(m\) is connected to spring and performs simple harmonic motion with a time period of \(2 s\). Another block \(B\) of mass \(m\) rests on \(A\). The coefficient of static friction betwwen \(A\) and \(B\) is \(\mu_{s}=0.6\). The maximum amplitude of oscillation which the system can have so that there is no relative motion between \(A\) and \(B\) is (take \(\pi^{2}=g=10\) )
supporting img

1 \(0.6\;m\)
2 \(0.3\;m\)
3 \(0.52\;m\)
4 \(0.4\;m\)
PHXI14:OSCILLATIONS

364403 A horizontal rod of mass \(m\) and length \(L\) is pivoted at one end. The rod's other end is supported by a spring of force constant \(k\). The rod is displaced by a small angle \(\theta\) from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is
supporting img

1 \(\sqrt{\dfrac{k}{3 m}}\)
2 \(\sqrt{\dfrac{3 k}{m}}\)
3 \(\sqrt{\dfrac{k}{m}}\)
4 \(\sqrt{\dfrac{3 k}{m}+\dfrac{3 g}{2 L}}\)
PHXI14:OSCILLATIONS

364404 Assertion :
The spring constant of a spring is \(k\). When it is divided into \(n\) equal parts, then spring constant of one piece is \(k{\rm{/}}n.\)
Reason :
The spring constant depends on material used for the spring.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI14:OSCILLATIONS

364405 Two bodies \(A\) and \(B\) of equal mass are suspended from two separate massles springs of force constant \(k_{1}\) and \(k_{2}\) respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body \(A\) to that of body \(B\) is

1 \(\sqrt{\dfrac{k_{2}}{k_{1}}}\)
2 \(\dfrac{k_{2}}{k_{1}}\)
3 \(\dfrac{k_{1}}{k_{2}}\)
4 \(\sqrt{\dfrac{k_{1}}{k_{2}}}\)
PHXI14:OSCILLATIONS

364406 A block \(A\) of mass \(m\) is connected to spring and performs simple harmonic motion with a time period of \(2 s\). Another block \(B\) of mass \(m\) rests on \(A\). The coefficient of static friction betwwen \(A\) and \(B\) is \(\mu_{s}=0.6\). The maximum amplitude of oscillation which the system can have so that there is no relative motion between \(A\) and \(B\) is (take \(\pi^{2}=g=10\) )
supporting img

1 \(0.6\;m\)
2 \(0.3\;m\)
3 \(0.52\;m\)
4 \(0.4\;m\)
PHXI14:OSCILLATIONS

364403 A horizontal rod of mass \(m\) and length \(L\) is pivoted at one end. The rod's other end is supported by a spring of force constant \(k\). The rod is displaced by a small angle \(\theta\) from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is
supporting img

1 \(\sqrt{\dfrac{k}{3 m}}\)
2 \(\sqrt{\dfrac{3 k}{m}}\)
3 \(\sqrt{\dfrac{k}{m}}\)
4 \(\sqrt{\dfrac{3 k}{m}+\dfrac{3 g}{2 L}}\)
PHXI14:OSCILLATIONS

364404 Assertion :
The spring constant of a spring is \(k\). When it is divided into \(n\) equal parts, then spring constant of one piece is \(k{\rm{/}}n.\)
Reason :
The spring constant depends on material used for the spring.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI14:OSCILLATIONS

364405 Two bodies \(A\) and \(B\) of equal mass are suspended from two separate massles springs of force constant \(k_{1}\) and \(k_{2}\) respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body \(A\) to that of body \(B\) is

1 \(\sqrt{\dfrac{k_{2}}{k_{1}}}\)
2 \(\dfrac{k_{2}}{k_{1}}\)
3 \(\dfrac{k_{1}}{k_{2}}\)
4 \(\sqrt{\dfrac{k_{1}}{k_{2}}}\)
PHXI14:OSCILLATIONS

364406 A block \(A\) of mass \(m\) is connected to spring and performs simple harmonic motion with a time period of \(2 s\). Another block \(B\) of mass \(m\) rests on \(A\). The coefficient of static friction betwwen \(A\) and \(B\) is \(\mu_{s}=0.6\). The maximum amplitude of oscillation which the system can have so that there is no relative motion between \(A\) and \(B\) is (take \(\pi^{2}=g=10\) )
supporting img

1 \(0.6\;m\)
2 \(0.3\;m\)
3 \(0.52\;m\)
4 \(0.4\;m\)
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PHXI14:OSCILLATIONS

364403 A horizontal rod of mass \(m\) and length \(L\) is pivoted at one end. The rod's other end is supported by a spring of force constant \(k\). The rod is displaced by a small angle \(\theta\) from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is
supporting img

1 \(\sqrt{\dfrac{k}{3 m}}\)
2 \(\sqrt{\dfrac{3 k}{m}}\)
3 \(\sqrt{\dfrac{k}{m}}\)
4 \(\sqrt{\dfrac{3 k}{m}+\dfrac{3 g}{2 L}}\)
PHXI14:OSCILLATIONS

364404 Assertion :
The spring constant of a spring is \(k\). When it is divided into \(n\) equal parts, then spring constant of one piece is \(k{\rm{/}}n.\)
Reason :
The spring constant depends on material used for the spring.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI14:OSCILLATIONS

364405 Two bodies \(A\) and \(B\) of equal mass are suspended from two separate massles springs of force constant \(k_{1}\) and \(k_{2}\) respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body \(A\) to that of body \(B\) is

1 \(\sqrt{\dfrac{k_{2}}{k_{1}}}\)
2 \(\dfrac{k_{2}}{k_{1}}\)
3 \(\dfrac{k_{1}}{k_{2}}\)
4 \(\sqrt{\dfrac{k_{1}}{k_{2}}}\)
PHXI14:OSCILLATIONS

364406 A block \(A\) of mass \(m\) is connected to spring and performs simple harmonic motion with a time period of \(2 s\). Another block \(B\) of mass \(m\) rests on \(A\). The coefficient of static friction betwwen \(A\) and \(B\) is \(\mu_{s}=0.6\). The maximum amplitude of oscillation which the system can have so that there is no relative motion between \(A\) and \(B\) is (take \(\pi^{2}=g=10\) )
supporting img

1 \(0.6\;m\)
2 \(0.3\;m\)
3 \(0.52\;m\)
4 \(0.4\;m\)