A wire of length 50 cm and weighing 10 gm is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 50 N/m and is stretched by 1 cm. If a wave pulse is produced on the string near the wall, then how much time will it take to reach the spring?

Options

A. 0.1 s
B. 0.2 s
C. 0.3 s
D. 0.4 s

Answer

A

Explanation

Tension in wire = kx = `50 xx 1/100 = 0.5 N`
Mass per unit length of string `mu = m/l`
` =10 xx 10^(-3) = 1/50 kgm^(-1) = 50 xx 10^(-2)`
speed of wave pulse on string
` v = sqrt(T/mu) = sqrt( (0.5)/((1/50)) ) = sqrt(25) ms^(-1) = 5ms^(-1)`
Time required by pulse to each other and
` t = l/v = (50 xx 10^(-2) m)/(5ms^(-1) ) = 0.1 s`