Some Systems Executing Simple Harmonic Motion
PHXI14:OSCILLATIONS

364445 Assertion :
When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Reason :
In standing position of girl, the length of the swing will increase.

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

364446 \(A\) and \(B\) are fixed points and the mass \(M\) is tied by strings at \(A\) and \(B\). If the mass \(M\) is displaced slightly out of this plane and released, it will execute oscillations with period. (Given, \(AM = BM = L,AB = 2\;d\) )
supporting img

1 \(2 \pi \sqrt{\dfrac{\left(L^{2}-d^{2}\right)^{1 / 2}}{g}}\)
2 \(2 \pi \sqrt{\dfrac{L}{g}}\)
3 \(2 \pi \sqrt{\dfrac{\left(2 d^{2}\right)^{3 / 2}}{g}}\)
4 \(2 \pi \sqrt{\dfrac{\left(L^{2}+d^{2}\right)^{1 / 2}}{g}}\)
PHXI14:OSCILLATIONS

364447 A simple pendulum has a time period \(T\) in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of material of the bob is :

1 \(\sqrt{\dfrac{7}{8}} T\)
2 \(\sqrt{\dfrac{5}{8}} T\)
3 \(\sqrt{\dfrac{3}{8}} T\)
4 \(\sqrt{\dfrac{8}{7}} T\)
PHXI14:OSCILLATIONS

364448 If pendulum bob on a \(2 m\) string is displaced \(60^{\circ}\) from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path?

1 \(\sqrt 2 \;m{s^{ - 1}}\)
2 \(\sqrt {2 \times 9.8} \;m{s^{ - 1}}\)
3 \(4.43\;m{s^{ - 1}}\)
4 \(1/\sqrt 2 \,m{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364449 Two light strings, each of length \(l\), are fixed at points \(A\) and \(B\) on a fixed horizontal rod \(xy\). A small bob is tied by both strings the strings are making angle \(45^{\circ}\) with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be:
supporting img

1 \(2 \pi \sqrt{\dfrac{\sqrt{2} l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{2 \sqrt{2} l}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{\sqrt{2} g}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g}}\)
PHXI14:OSCILLATIONS

364445 Assertion :
When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Reason :
In standing position of girl, the length of the swing will increase.

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

364446 \(A\) and \(B\) are fixed points and the mass \(M\) is tied by strings at \(A\) and \(B\). If the mass \(M\) is displaced slightly out of this plane and released, it will execute oscillations with period. (Given, \(AM = BM = L,AB = 2\;d\) )
supporting img

1 \(2 \pi \sqrt{\dfrac{\left(L^{2}-d^{2}\right)^{1 / 2}}{g}}\)
2 \(2 \pi \sqrt{\dfrac{L}{g}}\)
3 \(2 \pi \sqrt{\dfrac{\left(2 d^{2}\right)^{3 / 2}}{g}}\)
4 \(2 \pi \sqrt{\dfrac{\left(L^{2}+d^{2}\right)^{1 / 2}}{g}}\)
PHXI14:OSCILLATIONS

364447 A simple pendulum has a time period \(T\) in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of material of the bob is :

1 \(\sqrt{\dfrac{7}{8}} T\)
2 \(\sqrt{\dfrac{5}{8}} T\)
3 \(\sqrt{\dfrac{3}{8}} T\)
4 \(\sqrt{\dfrac{8}{7}} T\)
PHXI14:OSCILLATIONS

364448 If pendulum bob on a \(2 m\) string is displaced \(60^{\circ}\) from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path?

1 \(\sqrt 2 \;m{s^{ - 1}}\)
2 \(\sqrt {2 \times 9.8} \;m{s^{ - 1}}\)
3 \(4.43\;m{s^{ - 1}}\)
4 \(1/\sqrt 2 \,m{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364449 Two light strings, each of length \(l\), are fixed at points \(A\) and \(B\) on a fixed horizontal rod \(xy\). A small bob is tied by both strings the strings are making angle \(45^{\circ}\) with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be:
supporting img

1 \(2 \pi \sqrt{\dfrac{\sqrt{2} l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{2 \sqrt{2} l}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{\sqrt{2} g}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g}}\)
PHXI14:OSCILLATIONS

364445 Assertion :
When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Reason :
In standing position of girl, the length of the swing will increase.

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

364446 \(A\) and \(B\) are fixed points and the mass \(M\) is tied by strings at \(A\) and \(B\). If the mass \(M\) is displaced slightly out of this plane and released, it will execute oscillations with period. (Given, \(AM = BM = L,AB = 2\;d\) )
supporting img

1 \(2 \pi \sqrt{\dfrac{\left(L^{2}-d^{2}\right)^{1 / 2}}{g}}\)
2 \(2 \pi \sqrt{\dfrac{L}{g}}\)
3 \(2 \pi \sqrt{\dfrac{\left(2 d^{2}\right)^{3 / 2}}{g}}\)
4 \(2 \pi \sqrt{\dfrac{\left(L^{2}+d^{2}\right)^{1 / 2}}{g}}\)
PHXI14:OSCILLATIONS

364447 A simple pendulum has a time period \(T\) in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of material of the bob is :

1 \(\sqrt{\dfrac{7}{8}} T\)
2 \(\sqrt{\dfrac{5}{8}} T\)
3 \(\sqrt{\dfrac{3}{8}} T\)
4 \(\sqrt{\dfrac{8}{7}} T\)
PHXI14:OSCILLATIONS

364448 If pendulum bob on a \(2 m\) string is displaced \(60^{\circ}\) from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path?

1 \(\sqrt 2 \;m{s^{ - 1}}\)
2 \(\sqrt {2 \times 9.8} \;m{s^{ - 1}}\)
3 \(4.43\;m{s^{ - 1}}\)
4 \(1/\sqrt 2 \,m{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364449 Two light strings, each of length \(l\), are fixed at points \(A\) and \(B\) on a fixed horizontal rod \(xy\). A small bob is tied by both strings the strings are making angle \(45^{\circ}\) with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be:
supporting img

1 \(2 \pi \sqrt{\dfrac{\sqrt{2} l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{2 \sqrt{2} l}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{\sqrt{2} g}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g}}\)
PHXI14:OSCILLATIONS

364445 Assertion :
When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Reason :
In standing position of girl, the length of the swing will increase.

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

364446 \(A\) and \(B\) are fixed points and the mass \(M\) is tied by strings at \(A\) and \(B\). If the mass \(M\) is displaced slightly out of this plane and released, it will execute oscillations with period. (Given, \(AM = BM = L,AB = 2\;d\) )
supporting img

1 \(2 \pi \sqrt{\dfrac{\left(L^{2}-d^{2}\right)^{1 / 2}}{g}}\)
2 \(2 \pi \sqrt{\dfrac{L}{g}}\)
3 \(2 \pi \sqrt{\dfrac{\left(2 d^{2}\right)^{3 / 2}}{g}}\)
4 \(2 \pi \sqrt{\dfrac{\left(L^{2}+d^{2}\right)^{1 / 2}}{g}}\)
PHXI14:OSCILLATIONS

364447 A simple pendulum has a time period \(T\) in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of material of the bob is :

1 \(\sqrt{\dfrac{7}{8}} T\)
2 \(\sqrt{\dfrac{5}{8}} T\)
3 \(\sqrt{\dfrac{3}{8}} T\)
4 \(\sqrt{\dfrac{8}{7}} T\)
PHXI14:OSCILLATIONS

364448 If pendulum bob on a \(2 m\) string is displaced \(60^{\circ}\) from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path?

1 \(\sqrt 2 \;m{s^{ - 1}}\)
2 \(\sqrt {2 \times 9.8} \;m{s^{ - 1}}\)
3 \(4.43\;m{s^{ - 1}}\)
4 \(1/\sqrt 2 \,m{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364449 Two light strings, each of length \(l\), are fixed at points \(A\) and \(B\) on a fixed horizontal rod \(xy\). A small bob is tied by both strings the strings are making angle \(45^{\circ}\) with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be:
supporting img

1 \(2 \pi \sqrt{\dfrac{\sqrt{2} l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{2 \sqrt{2} l}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{\sqrt{2} g}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g}}\)
PHXI14:OSCILLATIONS

364445 Assertion :
When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Reason :
In standing position of girl, the length of the swing will increase.

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

364446 \(A\) and \(B\) are fixed points and the mass \(M\) is tied by strings at \(A\) and \(B\). If the mass \(M\) is displaced slightly out of this plane and released, it will execute oscillations with period. (Given, \(AM = BM = L,AB = 2\;d\) )
supporting img

1 \(2 \pi \sqrt{\dfrac{\left(L^{2}-d^{2}\right)^{1 / 2}}{g}}\)
2 \(2 \pi \sqrt{\dfrac{L}{g}}\)
3 \(2 \pi \sqrt{\dfrac{\left(2 d^{2}\right)^{3 / 2}}{g}}\)
4 \(2 \pi \sqrt{\dfrac{\left(L^{2}+d^{2}\right)^{1 / 2}}{g}}\)
PHXI14:OSCILLATIONS

364447 A simple pendulum has a time period \(T\) in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of material of the bob is :

1 \(\sqrt{\dfrac{7}{8}} T\)
2 \(\sqrt{\dfrac{5}{8}} T\)
3 \(\sqrt{\dfrac{3}{8}} T\)
4 \(\sqrt{\dfrac{8}{7}} T\)
PHXI14:OSCILLATIONS

364448 If pendulum bob on a \(2 m\) string is displaced \(60^{\circ}\) from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path?

1 \(\sqrt 2 \;m{s^{ - 1}}\)
2 \(\sqrt {2 \times 9.8} \;m{s^{ - 1}}\)
3 \(4.43\;m{s^{ - 1}}\)
4 \(1/\sqrt 2 \,m{s^{ - 1}}\)
PHXI14:OSCILLATIONS

364449 Two light strings, each of length \(l\), are fixed at points \(A\) and \(B\) on a fixed horizontal rod \(xy\). A small bob is tied by both strings the strings are making angle \(45^{\circ}\) with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be:
supporting img

1 \(2 \pi \sqrt{\dfrac{\sqrt{2} l}{g}}\)
2 \(2 \pi \sqrt{\dfrac{2 \sqrt{2} l}{g}}\)
3 \(2 \pi \sqrt{\dfrac{l}{\sqrt{2} g}}\)
4 \(2 \pi \sqrt{\dfrac{l}{g}}\)