Question

On a distant planet where the gravitational acceleration is 5.52 m/s^2, an astronaut hangs a 112-gram ball from the end of a wire. She observes the speed of transverse pulse along the wire to be 44.4 m/s. The linear density of the wire is closest to: (a) 0.131 g/m (b) 0.172 g/m (c) 0.227 g/m (d) 0.314 g/m (e) 0.462 g/s

Answer 1

Answer:

The linear density of the wire is 0.314 g/m.

Explanation:

It is given that,

Acceleration, $a=5.52\ m/s^2$

Mass of the ball, m = 112 gm

Speed of the transverse wave, v = 44.4 m/s

The speed of the transverse wave is given by :

$v=\sqrt{\dfrac{T}{\mu}}$

Where

T = tension in the wire

$\mu$ = mass per unit length

$\mu=\dfrac{T}{v^2}$

$\mu=\dfrac{ma}{v^2}$

$\mu=\dfrac{112\ g\times 5.52\ m/s^2}{(44.4\ m/s)^2}$

$\mu=0.3136\ g/m$

or

$\mu=0.314\ g/m$

So, the linear density of the wire is 0.314 g/m. Hence, this is the required solution.