The time period of oscillation of a simple pendulum having length L and mass of the bob m is given as T. If the length of the pendulum is increased to 4L and the mass of the bob is increased to 2m, then which one of the following is the new time period of

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Q: 41 (NDA-II/2018)
The time period of oscillation of a simple pendulum having length L and mass of the bob m is given as T. If the length of the pendulum is increased to 4L and the mass of the bob is increased to 2m, then which one of the following is the new time period of oscillation?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,22,8,1,22,2,5

keywords: 

{'pendulum': [0, 0, 0, 3], 'simple pendulum': [0, 0, 1, 4], 'oscillation': [0, 0, 1, 1], 'new time period': [0, 0, 0, 1], 'time period': [1, 0, 1, 12], '4l': [0, 0, 0, 1], 'mass': [0, 0, 2, 3], 'length': [0, 0, 1, 0], 'bob': [0, 0, 1, 2]}

Option 1: The time period of oscillation remains the same, T.

Option 2: The new time period of oscillation is 2T.

Option 3: The new time period of oscillation is 4T.

Option 4: The new time period of oscillation is T/2.

The correct answer is option 2: The new time period of oscillation is 2T.

When the length of the pendulum is increased to 4L, the time period of oscillation increases because the length of the pendulum is directly proportional to the time period. Similarly, when the mass of the bob is increased to 2m, the time period of oscillation increases because the mass of the bob is inversely proportional to the time period.

Therefore, when both the length and mass are increased, the time period of oscillation will be doubled. Thus, the new time period of oscillation is 2T.