Some Systems Executing Simple Harmonic Motion
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PHXI14:OSCILLATIONS

364467 Assertion :
For a simple pendulum the graph between \(g\) and \(T^{2}\) is hyperbola.
Reason :
\(T=2 \pi \sqrt{\dfrac{g}{l}}\)

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

364468 The ratio of frequencies of two oscillating pendulums are \(3: 2\). Their lengths are in the ratio

1 \(\sqrt{3}: \sqrt{2}\)
2 \(9: 4\)
3 \(4: 9\)
4 \(\sqrt{2}: \sqrt{3}\)
MHTCET - 2022
PHXI14:OSCILLATIONS

364469 In a seconds pendulum, mass of bob is \(30\;g\). If it is replaced by \(90\;g\) mass. Then its time period will be:-

1 \(2\,\sec \)
2 \(1\,\sec \)
3 \(3\,\sec \)
4 \(4\,\sec \)
PHXI14:OSCILLATIONS

364470 The bob of a simple pendulum of length \(L\) is released at time \(t = 0\) from a position of small angular displacement. Its linear displacement at time \(t\) is given by

1 \(x=a \sin \left(2 \pi \sqrt{\dfrac{L}{g}} t\right)\)
2 \(x=a \cos \left(2 \pi \sqrt{\dfrac{g}{L}} t\right)\)
3 \(x=a \sin \left(\sqrt{\dfrac{g}{L}} t\right)\)
4 \(x=a \cos \left(\sqrt{\dfrac{g}{L}} t\right)\)
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PHXI14:OSCILLATIONS

364467 Assertion :
For a simple pendulum the graph between \(g\) and \(T^{2}\) is hyperbola.
Reason :
\(T=2 \pi \sqrt{\dfrac{g}{l}}\)

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

364468 The ratio of frequencies of two oscillating pendulums are \(3: 2\). Their lengths are in the ratio

1 \(\sqrt{3}: \sqrt{2}\)
2 \(9: 4\)
3 \(4: 9\)
4 \(\sqrt{2}: \sqrt{3}\)
MHTCET - 2022
PHXI14:OSCILLATIONS

364469 In a seconds pendulum, mass of bob is \(30\;g\). If it is replaced by \(90\;g\) mass. Then its time period will be:-

1 \(2\,\sec \)
2 \(1\,\sec \)
3 \(3\,\sec \)
4 \(4\,\sec \)
PHXI14:OSCILLATIONS

364470 The bob of a simple pendulum of length \(L\) is released at time \(t = 0\) from a position of small angular displacement. Its linear displacement at time \(t\) is given by

1 \(x=a \sin \left(2 \pi \sqrt{\dfrac{L}{g}} t\right)\)
2 \(x=a \cos \left(2 \pi \sqrt{\dfrac{g}{L}} t\right)\)
3 \(x=a \sin \left(\sqrt{\dfrac{g}{L}} t\right)\)
4 \(x=a \cos \left(\sqrt{\dfrac{g}{L}} t\right)\)
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PHXI14:OSCILLATIONS

364467 Assertion :
For a simple pendulum the graph between \(g\) and \(T^{2}\) is hyperbola.
Reason :
\(T=2 \pi \sqrt{\dfrac{g}{l}}\)

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

364468 The ratio of frequencies of two oscillating pendulums are \(3: 2\). Their lengths are in the ratio

1 \(\sqrt{3}: \sqrt{2}\)
2 \(9: 4\)
3 \(4: 9\)
4 \(\sqrt{2}: \sqrt{3}\)
MHTCET - 2022
PHXI14:OSCILLATIONS

364469 In a seconds pendulum, mass of bob is \(30\;g\). If it is replaced by \(90\;g\) mass. Then its time period will be:-

1 \(2\,\sec \)
2 \(1\,\sec \)
3 \(3\,\sec \)
4 \(4\,\sec \)
PHXI14:OSCILLATIONS

364470 The bob of a simple pendulum of length \(L\) is released at time \(t = 0\) from a position of small angular displacement. Its linear displacement at time \(t\) is given by

1 \(x=a \sin \left(2 \pi \sqrt{\dfrac{L}{g}} t\right)\)
2 \(x=a \cos \left(2 \pi \sqrt{\dfrac{g}{L}} t\right)\)
3 \(x=a \sin \left(\sqrt{\dfrac{g}{L}} t\right)\)
4 \(x=a \cos \left(\sqrt{\dfrac{g}{L}} t\right)\)
NEET DIGITAL LIBRARY
PHXI14:OSCILLATIONS

364467 Assertion :
For a simple pendulum the graph between \(g\) and \(T^{2}\) is hyperbola.
Reason :
\(T=2 \pi \sqrt{\dfrac{g}{l}}\)

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

364468 The ratio of frequencies of two oscillating pendulums are \(3: 2\). Their lengths are in the ratio

1 \(\sqrt{3}: \sqrt{2}\)
2 \(9: 4\)
3 \(4: 9\)
4 \(\sqrt{2}: \sqrt{3}\)
MHTCET - 2022
PHXI14:OSCILLATIONS

364469 In a seconds pendulum, mass of bob is \(30\;g\). If it is replaced by \(90\;g\) mass. Then its time period will be:-

1 \(2\,\sec \)
2 \(1\,\sec \)
3 \(3\,\sec \)
4 \(4\,\sec \)
PHXI14:OSCILLATIONS

364470 The bob of a simple pendulum of length \(L\) is released at time \(t = 0\) from a position of small angular displacement. Its linear displacement at time \(t\) is given by

1 \(x=a \sin \left(2 \pi \sqrt{\dfrac{L}{g}} t\right)\)
2 \(x=a \cos \left(2 \pi \sqrt{\dfrac{g}{L}} t\right)\)
3 \(x=a \sin \left(\sqrt{\dfrac{g}{L}} t\right)\)
4 \(x=a \cos \left(\sqrt{\dfrac{g}{L}} t\right)\)
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