Q. No.If \(T_1,T_2,T_3,T_4\) and \(T_5\) represent the tension in the string of a simple pendulum when the bob is at the left extreme, right extreme, mean, any intermediate left and any intermediate right positions, respectively. Then, which of the following relations are correct?
(A) \(T_1=T_2\)
(B) \(T_3>T_2\)
(C) \(T_4>T_3\)
(D) \(T_3=T_4\)
(E) \(T_5>T_2\)
Choose the most appropriate answer from the options given below:
(A) \(T_1=T_2\)
(B) \(T_3>T_2\)
(C) \(T_4>T_3\)
(D) \(T_3=T_4\)
(E) \(T_5>T_2\)
Choose the most appropriate answer from the options given below:
| 1. | (A), (B) and (C) only |
| 2. | (B), (C) and (D) only |
| 3. | (A), (B) and (E) only |
| 4. | (C), (D) and (E) only |
Subtopic: Angular SHM |
67%
From NCERT
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The time period of a simple pendulum in a stationary lift is \(T.\) If the lift accelerates with \(\dfrac g 6\) vertically upwards, then the time period will be: (Where \(g=\) acceleration due to gravity)
| 1. | \(\sqrt{\dfrac{6}{5}} ~T \) | 2. | \(\sqrt{\dfrac{5}{6}} ~T\) |
| 3. | \(\sqrt{\dfrac{6}{7}}~T\) | 4. | \(\sqrt{\dfrac{7}{6}} ~T\) |
Subtopic: Angular SHM |
81%
From NCERT
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If a simple pendulum is brought deep inside a mine from the earth's surface, its time period of oscillation will:
| 1. | increase |
| 2. | decrease |
| 3. | remain same |
| 4. | any of the above depending on the length of the pendulum |
Subtopic: Angular SHM |
68%
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If a simple pendulum be suspended in an elevator which is moving upward, its time period is found to decrease by \(2\%\). The acceleration of the elevator is (in magnitude):
| 1. | \(2\)% of \(g\) | 2. | \(1\)% of \(g\) |
| 3. | \(4\)% of \(g\) | 4. | \(102\)% of \(g\) |
Subtopic: Angular SHM |
77%
From NCERT
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Motion of a simple pendulum executing simple harmonic motion is represented by the following equation;
\({y}=\mathrm{A} \sin (\pi {t}+\phi)\), where time is measured in seconds. The length of the pendulum is:
1. \(97.23\) cm
2. \(25.3\) cm
3. \(99.4\) cm
4. \(406.1\) cm
\({y}=\mathrm{A} \sin (\pi {t}+\phi)\), where time is measured in seconds. The length of the pendulum is:
1. \(97.23\) cm
2. \(25.3\) cm
3. \(99.4\) cm
4. \(406.1\) cm
Subtopic: Angular SHM |
82%
From NCERT
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A simple pendulum bob is a hollow sphere full of sand suspended by means of a wire. If all the sand is drained out immediately, then the time period of the pendulum will:
| 1. | increase | 2. | decrease |
| 3. | remain same | 4. | become erratic |
Subtopic: Angular SHM |
62%
From NCERT
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The length of a seconds pendulum at a height \(h=2R\) from the earth's surface will be:
(Given \(R=\) Radius of the earth and acceleration due to gravity at the surface of the earth \(g = \pi^2 \) m/s2)
1. \({\dfrac 2 9} \) m
2. \({\dfrac 4 9} \) m
3. \({\dfrac 8 9} \) m
4. \({\dfrac 1 9} \) m
(Given \(R=\) Radius of the earth and acceleration due to gravity at the surface of the earth \(g = \pi^2 \) m/s2)
1. \({\dfrac 2 9} \) m
2. \({\dfrac 4 9} \) m
3. \({\dfrac 8 9} \) m
4. \({\dfrac 1 9} \) m
Subtopic: Angular SHM |
74%
From NCERT
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The metallic bob of a simple pendulum has a relative density equal to \(5\). The time period of this pendulum is \(10~\mathrm{s}\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt x ~\mathrm{s}\). The value of \(x\) will be:
1. \(5\)
2. \(7\)
3. \(9\)
4. \(2\)
1. \(5\)
2. \(7\)
3. \(9\)
4. \(2\)
Subtopic: Angular SHM |
72%
From NCERT
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A simple pendulum hanging from the ceiling of a stationary lift has a time period \(T_1\). When the lift moves downward with constant velocity, then the time period becomes \(T_2\). It can be concluded that:
| 1. | \(T_2 ~\text{is infinity} \) | 2. | \(T_2>T_1 \) |
| 3. | \(T_2<T_1 \) | 4. | \(T_2=T_1\) |
Subtopic: Angular SHM |
62%
From NCERT
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A pendulum clock that keeps the correct time on the earth is taken to the moon. It will run: (Take \(g_{\text{moon}}=\dfrac{g_\text{earth}}{6}\))
| 1. | at the correct rate | 2. | \(6\) times faster |
| 3. | \(\sqrt6\) times faster | 4. | \(\sqrt6\) times slower |
Subtopic: Angular SHM |
51%
From NCERT
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