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 job is increased to 2m, then which one of the following is the new time period of oscillation?a)Tb)2Tc)4Td)T/2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

The time period of oscillation of a simple pendulum is given by the formula:

T = 2π√(L/g)

Where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.

Now, let's consider the first scenario where the length of the pendulum is L and the mass of the bob is m. The time period of oscillation in this case is T.

Next, let's consider the second scenario where the length of the pendulum is 4L and the mass of the bob is 2m. We need to find the new time period of oscillation in this case.

Let's substitute the values into the formula and calculate the new time period:

T' = 2π√(4L/g) = 2π(2√(L/g)) = 4π√(L/g)

Therefore, the new time period of oscillation in this scenario is 4T.

From the given options, we can see that the correct answer is option B, which states that the new time period is 2T. However, this is not correct.

The correct answer is option C, which states that the new time period is 4T.

Explanation:
- The time period of a simple pendulum is directly proportional to the square root of the length of the pendulum.
- When the length of the pendulum is increased to 4L, the time period is multiplied by √4 = 2.
- The time period is also directly proportional to the square root of the mass of the bob.
- When the mass of the bob is increased to 2m, the time period is multiplied by √2.
- Therefore, the overall effect is that the new time period is 4 times the original time period.

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