A man weighing `60kg` stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude `0.1m` and frequency `(2)/(pi)`Hz. Which of the following statement is correct ?

Options

A. The spring balance reads the weight of man as `60kg`
B. The spring balance reading fluctuates between `60kg` and `70kg`
C. The spring balance reading fluctuates bettween `50kg` and `60kg`
D. The spring balance reading fluctuates between `50kg` and `70kg`

Answer

D

Explanation

The maximum force acting on the body executing simple harmonic motion is
`m omega^(2) = m xx (2 pi f)^(2) a = 60 xx (2pi xx (2)/(pi))^(2) xx 0.1 N`
`= 60 xx 16 xx 0.1 = 96N =- (96)/(9.8) = 10 kgf ` and this force is toward mean postion

The reaction of the on the platform away from the mean position it reduition the weight of men on upper exetreme i.e. net weight `= (60 - 10)kgf`
This force adds to the weight at lower exetreme position i.e. net weifght become `= (60 + 10)kgf`.
Therefore the reading the weight recording by spring balance fluctes between `50 kgf` and 70 kgf`.