A bob of mass m is suspended from a string of length L, forming a pendulum. The

Question

A bob of mass m is suspended from a string of length L, forming a pendulum. The period of this pendulum is 4.0 s. If the pendulum bob is replaced with one of mass 1/3 m and the length of the pendulum is increased to 2L, what is the period of oscillation? A bob of mass m is suspended from a string of length L, forming a pendulum. The period of this pendulum is 4.0 s. If the pendulum bob is replaced with one of mass 1/3 m and the length of the pendulum is increased to 2L, what is the period of oscillation? A bob of mass m is suspended from a string of length L, forming a pendulum. The period of this pendulum is 4.0 s. If the pendulum bob is replaced with one of mass 1/3 m and the length of the pendulum is increased to 2L, what is the period of oscillation?

Explanation / Answer

Period of a pendulum is given by:

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

we can see that period of pendulum does not depends on mass

Since g is constant, So T is directly proportional to square root of length

T2/T1 = sqrt (L2/L1)

T2 = T1*sqrt (L2/L1)

T2 = 4*sqrt (2L/L)

T2 = 4*sqrt 2

T2 = 5.66 sec

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