Apendulum oscillates with a period t. if both the mass of the bob and the length of the pendulum are doubled, the new period will be. a. 4tb. square root 2tc. td. t/square root 2e. t/4

Explanation:

First let us write out the formula connecting the simple parameters in a system of simple pendulum

Where

T= period of oscillation,

L=length of the pendulum

g= acceleration due to gravity

from the above formula, it is obvious that Mass has no effect on the period(T).

Again let see the relationship that exist between the period(T) and the length(L).

let assume , then we can have

We can conclude that the period is directly proportional to the square-root of the length.

we can vary the constant K to have

Now back to the question, if the length was  doubled, we have the

using the varying equation, we can substitute values and arrive at

carrying out simple operation, we arrive at

Finally we have

hence we can conclude that the When the length is doubled, the period is increase by a factor of root 2

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