Some Systems Executing Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364463 The measured value of length of a simple pendulum is \(20\,cm\) with \(2\,mm\) accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \({N \%}\). The value of \({N}\) is

1 8
2 5
3 4
4 6
JEE - 2024
PHXI14:OSCILLATIONS

364464 A man measures the period of a simple pendulum inside a stationary lift and finds it to be \(T\) second. If the accelerates upwards with an accelerating \(\frac{g}{4}\), then the period of the pendulum will be

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

364465 If a simple pendulum of length \(\ell\) has maximum angular displacment \(\theta\), then the maximum kinetic energy of the bob of mass \(m\) is

1 \(\left(\dfrac{1}{2}\right)\left(\dfrac{m g}{\ell}\right)\)
2 \(\left(\dfrac{1}{2}\right) m \sqrt{\dfrac{\ell}{g}}\)
3 \((1 / 2) m g \ell \sin \theta\)
4 \(m g \ell(1-\cos \theta)\)
PHXI14:OSCILLATIONS

364466 The period of oscillation of a simple pendulum of length \(l\) suspended from the roof of the vehicle which moves down without friction on an inclined plane of inclination \(\alpha\), is given by:

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

364463 The measured value of length of a simple pendulum is \(20\,cm\) with \(2\,mm\) accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \({N \%}\). The value of \({N}\) is

1 8
2 5
3 4
4 6
JEE - 2024
PHXI14:OSCILLATIONS

364464 A man measures the period of a simple pendulum inside a stationary lift and finds it to be \(T\) second. If the accelerates upwards with an accelerating \(\frac{g}{4}\), then the period of the pendulum will be

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

364465 If a simple pendulum of length \(\ell\) has maximum angular displacment \(\theta\), then the maximum kinetic energy of the bob of mass \(m\) is

1 \(\left(\dfrac{1}{2}\right)\left(\dfrac{m g}{\ell}\right)\)
2 \(\left(\dfrac{1}{2}\right) m \sqrt{\dfrac{\ell}{g}}\)
3 \((1 / 2) m g \ell \sin \theta\)
4 \(m g \ell(1-\cos \theta)\)
PHXI14:OSCILLATIONS

364466 The period of oscillation of a simple pendulum of length \(l\) suspended from the roof of the vehicle which moves down without friction on an inclined plane of inclination \(\alpha\), is given by:

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

364463 The measured value of length of a simple pendulum is \(20\,cm\) with \(2\,mm\) accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \({N \%}\). The value of \({N}\) is

1 8
2 5
3 4
4 6
JEE - 2024
PHXI14:OSCILLATIONS

364464 A man measures the period of a simple pendulum inside a stationary lift and finds it to be \(T\) second. If the accelerates upwards with an accelerating \(\frac{g}{4}\), then the period of the pendulum will be

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

364465 If a simple pendulum of length \(\ell\) has maximum angular displacment \(\theta\), then the maximum kinetic energy of the bob of mass \(m\) is

1 \(\left(\dfrac{1}{2}\right)\left(\dfrac{m g}{\ell}\right)\)
2 \(\left(\dfrac{1}{2}\right) m \sqrt{\dfrac{\ell}{g}}\)
3 \((1 / 2) m g \ell \sin \theta\)
4 \(m g \ell(1-\cos \theta)\)
PHXI14:OSCILLATIONS

364466 The period of oscillation of a simple pendulum of length \(l\) suspended from the roof of the vehicle which moves down without friction on an inclined plane of inclination \(\alpha\), is given by:

1 \(\pi \sqrt{\dfrac{l}{g \cos \alpha}}\)
2 \(2 \pi \sqrt{\dfrac{l}{g \cos \alpha}}\)
3 \(\dfrac{1}{\pi} \sqrt{\dfrac{l}{2 g \cos \alpha}}\)
4 \(\dfrac{1}{2 \pi} \sqrt{\dfrac{l}{g \cos \alpha}}\)
For More Updates join with Us
PHXI14:OSCILLATIONS

364463 The measured value of length of a simple pendulum is \(20\,cm\) with \(2\,mm\) accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \({N \%}\). The value of \({N}\) is

1 8
2 5
3 4
4 6
JEE - 2024
PHXI14:OSCILLATIONS

364464 A man measures the period of a simple pendulum inside a stationary lift and finds it to be \(T\) second. If the accelerates upwards with an accelerating \(\frac{g}{4}\), then the period of the pendulum will be

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

364465 If a simple pendulum of length \(\ell\) has maximum angular displacment \(\theta\), then the maximum kinetic energy of the bob of mass \(m\) is

1 \(\left(\dfrac{1}{2}\right)\left(\dfrac{m g}{\ell}\right)\)
2 \(\left(\dfrac{1}{2}\right) m \sqrt{\dfrac{\ell}{g}}\)
3 \((1 / 2) m g \ell \sin \theta\)
4 \(m g \ell(1-\cos \theta)\)
PHXI14:OSCILLATIONS

364466 The period of oscillation of a simple pendulum of length \(l\) suspended from the roof of the vehicle which moves down without friction on an inclined plane of inclination \(\alpha\), is given by:

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