(a) if a pendulum has period T and you double its length, what is its new period

Question

(a) if a pendulum has period T and you double its length, what is its new period in terms of T? (b) If a pendulum has a length L and you want to triple its frequency, what should be its length in terms of L? (c) Suppose a pendulum has a length L and period T on earth. If you take it to a planet where the acceleration of freely falling objects is ten times what it is on earth, what should you do to the length to keep the period the same as on earth? (d) If you do not change the pendulum's length in part (c), what is its period on that planet in terms of T? (e) If a pendulum has a period T and you triple the mass of its bob, what happens to the period (in terms of T)?

Explanation / Answer

(a) As, (T = 2pi sqrt{Lover g} ) ---------(1) (L_{new} = 2L) ( T_{new} = sqrt{2} T) (b) we want, (f_{new} = 3 f = 3/T) or (T_{new} = T/3) => (L_{new} = L/9) (c) from eq. (1): for keeping the same T ; L should be increased in same factor. i.e. (L_{new} = 10 L) (d) (T_{new} = rac{T}{sqrt{10}}) (e) Time period of pendulum does not depend on it's mass. => (T_{new} = T)

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