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The time period of a pendulum on earth is 2 seconds. What will be the time period of the same pendulum on a planet having acceleration due to gravity 9 times of earth?

The time period of a pendulum on earth is 2 seconds. What will be the time period of the same pendulum on a planet having acceleration due to gravity 9 times of earth? Correct Answer  2/3 seconds

CONCEPT:

  • The time period of the pendulum having the length of string l is given as

T = 2 π √ (l/g) -- (1)

g is the acceleration due to gravity.

CALCULATION:

The acceleration due to gravity on planet having acceleration due to gravity 9 times of earth 

g' = 9g 

Time period of pendulum on new planet will be

T' = 2 π √ (l / g')

= 2 π √ (l / 9g) 

= 2 π √ (l / g) / √ 9

= 2 π √ (l / g) / 3

=  T / 3 (using eq 1)

Given time period on earth is 2 sec

Time period on the planet will be T / 3 sec = 2 / 3 sec

So, answer is 2 / 3 second.

EXTRA POINTS:

  • The time period of the pendulum is independent of mass.

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