A simple pendulum that consists of a small ball of mass m and a massless wire of

Question

A simple pendulum that consists of a small ball of mass m and a massless wire of length L swings with a period T. Suppose now that the mass is rearranged so that mass of the ball was reduced but the mass of the wire was increased, with the total mass remaining m and the length being L. What is true about the new period of swing? (There could be more than one correct choice.)

EDIT- i answer A (only A) is wrong

A. The new period is T because the length L has not changed. B. The new period is greater than T. C. The new period is T because the total mass m has not changed. D. The new period is T because neither L nor m have changed. E. The new period is less than T

Explanation / Answer

initially, T = 2pi sqrt(L/g)

finally,

I = (m1 L^2 / 3) + (m2 L^2)

suppose center of mass is at L'

L/2 < L' < L

T = 2pi sqrt[ I / m g L' ]

T = 2 pi sqrt [ (m1 L^2 / 3) + (m2 L^2) / m g L' ]

= 2 pi sqrt[ L^2 (m1/3 + m2) / m g L' ]

L^2 (m1/3 + m2) / m g L' : L/g

(L / L') ((m1/3 + m2)/m ) ( L / g) : L/g

now we have to check whether (L / L') ((m1/3 + m2)/m ) is greater than or less than 1.

L' = (m1 L / 2) + (m2 L) / (m )

L / L' = m / (m1/2 + m2)

term = m1/3 + m2 / m1/2 + m2 < 1

hence new time period will be less than old time period.

Ans(E)

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