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# The time period of a spring pendulum on earth is T. If it is taken on the mean and made to oscillate the period of vibration will be (A) Less than T(B) Equal to T(C) More than T(D) None of these

Last updated date: 16th Sep 2024
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Hint: In this type of problem, first we have to remember the expression for the time period of the pendulum and check the dependency of time period with mass m, spring constant k and gravitational acceleration g.

Step by step answer: We know that the time period of spring pendulum on earth is given as $T = 2\pi \sqrt {\dfrac{m}{k}}$
Where
m $=$ mass of pendulum
k $=$ spring constant
From expression of time period, we can easily see that time period T. depends on mass of body in pendulum and spring constant k.
Time period of the pendulum does not depend on the gravitational acceleration g.
We know that when we take the pendulum at the moon then only gravitational acceleration g will change.
But the time period does not depend on g. So the time period remains the same.
Hence (B) is correct answer i.e., Equal to T

Note: In many problems of spring they can ask about the spring constant when spring is cutting into many parts.
When any spring is cut into n parts having spring constant k then the product of k and length of spring $\ell$ remains constant.
$k\ell =$constant