A certain frictionless simple pendulum having a length L and mass Mswings with period T. If both L and M are doubled, what is the new period? a. 2T
b. T/4
c. √2T
d. T
e. 4T

C.√2T

Explanation:

The period of a new pendulum is expressed as;

T = 2π√L/g 1

L is the length of the string

g is the acceleration due to gravity

If the length is doubled, the new length L2 = 2L

T2 = 2π√2L/g 2

Divide equation 2 by 1;

T2/T = (2π√2L/g)/(2π√L/g)

T2/T = √2L/g * √g/L

T2/T = √2L/L

T2/T = √2

T2 = √2T

Hence its new period will be √2T

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