Question

A taut string of length 1.0 m is holding a yo-yo of mass 130 grams. You notice from flicking the top of the string that the pulse takes 66 ms to travel down to the yo-yo. What is the mass of the string

Answer 1

m = 5.54 grams.

Step-by-step explanation:

It is given that,

Length of a string, l = 1 m

Mass, m = 130 g = 0.13 kg

Time, t = 66 ms = 0.066 s

The speed of a wave is given by :

`v=\sqrt{(T)/(\mu)}`

T is tension, T = mg

T = 0.13 kg × 9.8 m/s² = 1.274 N

`\mu` is mass per unit length,
`\mu=(m)/(l)`

Let t is time. It can be given by :

`t=(l)/(v)\\\\t=\frac{l}{\sqrt{(T)/((m/l))} }\\\\m=(Tt^2)/(l)\\\\m=(1.274* 0.066^2)/(1)\\\\m=0.00554\ kg`

or

m = 5.54 grams

So, the mass of the string is 5.54 grams.