A vertical block-spring system on earth has a period of 6.0 s. What is the period of this same system on the moon where the acceleration due to gravity is roughly 1/6 that of earth? A) 1.0s B) 2.4s C) 6.0s D) 15s E) 36s

D) 15s

Explanation:

let Te be the period of the block-spring system on earth and Tm be the period of the same system on the moon. let g1 be the gravitational acceleration on earth and g2 be the gravitational acceleration on the moon.

the period of a pendulum is given by:

T = 2π√ (L/g)

so on earth:

Te = 2π√ (L/g1)

= 6s

on the moon;

Tm = 2π√ (L/g2)

since g2 = 1/6 g1 then:

Tm = 2π√ (L / (1/6*g1))

= √ (6) * 2π√ (L / (g1))

and 2π√ (L / (g1)) = Te = 6s

Tm = (√ (6)) * 6 = 14.7s ≈ 15s

Therefore, the period of the block-spring system on the moon is 15s.