SATHEE: Oscillations - Result Question 53

Oscillations - Result Question 53

57. Two simple pendulums of length $5 m$ and $20 m$ respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations

[1998]

(a) 5

(b) 1

(d) 3

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Answer:

Correct Answer: 57. (c)

Solution:

(c) Let the pendulums be in phase after $t s e c$ of start. Within this time, if the bigger pendulum executes $n$ oscillations, the smaller one will have executed $(n + 1)$ oscillations.

Now, the time of $n$ oscillation $= 2 π \sqrt{\frac{20}{g}} \times n$

& the time of $(n + 1)$ oscillation

$= 2 π \sqrt{\frac{5}{g}} \times (n + 1)$

To be in phase

$2 π \sqrt{\frac{20}{g}} \times n = 2 π \sqrt{\frac{5}{g}} \times (n + 1)$

or, $2 n = n + 1$

or, $n = 1$

Hence, the no. of oscillations executed by shorter pendulum $= n + 1 = 1 + 1 = 2$

58 .

$n^{'} = \frac{1}{2 π} \sqrt{\frac{k}{4 m}} = \frac{1}{2} \times \frac{1}{2 π} \sqrt{\frac{k}{m}}$

On putting the value of $n$ we get $n^{'} = \frac{n}{2}$

Oscillations - Result Question 53

57. Two simple pendulums of length $5 m$ and $20 m$ respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations

Answer:

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Oscillations - Result Question 53

57. Two simple pendulums of length 5m and 20m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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57. Two simple pendulums of length $5 m$ and $20 m$ respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed oscillations