# If the mass of the bob of a pendulum is increased by a factor of 3, the period of the pendulum motion will ? A) increase by a factor of 2  b) remain the same c) be decreased by a factor of 2 or 4.

Lupe Tanner, Ph.D. | Certified Educator

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The time period of a pendulum is a function of its length only and does not depend on the mass of its bob. Mathematically, the time period of a pendulum can be written as:

`T = 2pi sqrt(L/g)`

where T is the time period of the pendulum, L is the pendulum length and g is the acceleration due to gravity. Hence, time period of a pendulum is independent of the mass of its bob.

Thus, if we increase the mass of the bob of a pendulum by a factor of 3, its time period will remain unchanged. Option (b) is correct.

On the other hand, if we changed the length of the pendulum by a factor of 3, say increased it by a factor of 3, its time period will increase by a factor of `sqrt (3)` .

Hope this helps.