Some Systems Executing Simple Harmonic Motion
PHXI14:OSCILLATIONS

364471 Assertion :
The frequency of a second pendulum in an elevator moving up with an acceleration half the acceleration due to gravity is \(0.612\,{s^{ - 1}}\).
Reason :
The frequency of a second pendulum does not depend upon acceleration due to gravity.

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

364472 A pendulum has time period \(T\) for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings in the left of its resting position as shown in figure. The pendulum is released from rest at a certain point \(A\). The time taken by it to return to the point \(A\) is
supporting img

1 \(T / 2\)
2 \(T\)
3 \(T / 4\)
4 \(3 T / 4\)
PHXI14:OSCILLATIONS

364473 If \({R}\) is the radius of the earth and the acceleration due to gravity on the surface of earth is \({g=\pi^{2} {~m} / {s}^{2}}\), then the length of the second's pendulum at a height \({h=2 R}\) from the surface of earth will be

1 \({\dfrac{8}{9} m}\)
2 \({\dfrac{4}{9} m}\)
3 \({\dfrac{2}{9} m}\)
4 \({\dfrac{1}{9} m}\)
PHXI14:OSCILLATIONS

364474 Simple pendulum is executing simple harmonic motion with time period \(T\). If the length of the pendulum is increased by \(21 \%\), then percentage increase in the time period of the pendulum is:

1 \(13 \%\)
2 \(22 \%\)
3 \(10 \%\)
4 \(50 \%\)
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PHXI14:OSCILLATIONS

364471 Assertion :
The frequency of a second pendulum in an elevator moving up with an acceleration half the acceleration due to gravity is \(0.612\,{s^{ - 1}}\).
Reason :
The frequency of a second pendulum does not depend upon acceleration due to gravity.

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

364472 A pendulum has time period \(T\) for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings in the left of its resting position as shown in figure. The pendulum is released from rest at a certain point \(A\). The time taken by it to return to the point \(A\) is
supporting img

1 \(T / 2\)
2 \(T\)
3 \(T / 4\)
4 \(3 T / 4\)
PHXI14:OSCILLATIONS

364473 If \({R}\) is the radius of the earth and the acceleration due to gravity on the surface of earth is \({g=\pi^{2} {~m} / {s}^{2}}\), then the length of the second's pendulum at a height \({h=2 R}\) from the surface of earth will be

1 \({\dfrac{8}{9} m}\)
2 \({\dfrac{4}{9} m}\)
3 \({\dfrac{2}{9} m}\)
4 \({\dfrac{1}{9} m}\)
PHXI14:OSCILLATIONS

364474 Simple pendulum is executing simple harmonic motion with time period \(T\). If the length of the pendulum is increased by \(21 \%\), then percentage increase in the time period of the pendulum is:

1 \(13 \%\)
2 \(22 \%\)
3 \(10 \%\)
4 \(50 \%\)
PHXI14:OSCILLATIONS

364471 Assertion :
The frequency of a second pendulum in an elevator moving up with an acceleration half the acceleration due to gravity is \(0.612\,{s^{ - 1}}\).
Reason :
The frequency of a second pendulum does not depend upon acceleration due to gravity.

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

364472 A pendulum has time period \(T\) for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings in the left of its resting position as shown in figure. The pendulum is released from rest at a certain point \(A\). The time taken by it to return to the point \(A\) is
supporting img

1 \(T / 2\)
2 \(T\)
3 \(T / 4\)
4 \(3 T / 4\)
PHXI14:OSCILLATIONS

364473 If \({R}\) is the radius of the earth and the acceleration due to gravity on the surface of earth is \({g=\pi^{2} {~m} / {s}^{2}}\), then the length of the second's pendulum at a height \({h=2 R}\) from the surface of earth will be

1 \({\dfrac{8}{9} m}\)
2 \({\dfrac{4}{9} m}\)
3 \({\dfrac{2}{9} m}\)
4 \({\dfrac{1}{9} m}\)
PHXI14:OSCILLATIONS

364474 Simple pendulum is executing simple harmonic motion with time period \(T\). If the length of the pendulum is increased by \(21 \%\), then percentage increase in the time period of the pendulum is:

1 \(13 \%\)
2 \(22 \%\)
3 \(10 \%\)
4 \(50 \%\)
PHXI14:OSCILLATIONS

364471 Assertion :
The frequency of a second pendulum in an elevator moving up with an acceleration half the acceleration due to gravity is \(0.612\,{s^{ - 1}}\).
Reason :
The frequency of a second pendulum does not depend upon acceleration due to gravity.

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

364472 A pendulum has time period \(T\) for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings in the left of its resting position as shown in figure. The pendulum is released from rest at a certain point \(A\). The time taken by it to return to the point \(A\) is
supporting img

1 \(T / 2\)
2 \(T\)
3 \(T / 4\)
4 \(3 T / 4\)
PHXI14:OSCILLATIONS

364473 If \({R}\) is the radius of the earth and the acceleration due to gravity on the surface of earth is \({g=\pi^{2} {~m} / {s}^{2}}\), then the length of the second's pendulum at a height \({h=2 R}\) from the surface of earth will be

1 \({\dfrac{8}{9} m}\)
2 \({\dfrac{4}{9} m}\)
3 \({\dfrac{2}{9} m}\)
4 \({\dfrac{1}{9} m}\)
PHXI14:OSCILLATIONS

364474 Simple pendulum is executing simple harmonic motion with time period \(T\). If the length of the pendulum is increased by \(21 \%\), then percentage increase in the time period of the pendulum is:

1 \(13 \%\)
2 \(22 \%\)
3 \(10 \%\)
4 \(50 \%\)