In the arrangement shown in Fig. 7.100 , mass can be hung from a string with a linear mass density of `2 xx 10^(-3) kg//m` that passes over a light pulley . The string is connected to a vibrator of frequency `700 Hz` and the length of the string between the vibrator and the pulley is `1 m`.

If the standing waves are observed , the largest mass to be hung is

Options

A. `16 kg`
B. `25 kg`
C. `32 kg`
D. `400 kg`

Answer

D

Explanation

For largest mass , `p = 1`
`n = (p)/( 2L) sqrt((T)/(mu))`
`700 = (p)/( 2L) sqrt((T)/(mu))`
` m = 2 xx 10^(-3) kg//m , L = 1 m`
`T = [ ( 700)^(2) xx 4 xx 1 xx 2 xx 10^(-3)] = 3920 N`
Largest mass to be hang , `M_(max) = 3920//9.8 = 400 kg`