Answer:
[tex]t=2.08*10^{-3}seconds\\ t=2.08 milliseconds[/tex]
Explanation:
Given Data
Mass= 0.55g = 0.00055 kg
length=1.2 m
diameter=0.0020 mm
density=1300[tex]\frac{kg}{m^{3} }[/tex]
time=?
Solution
[tex]V=\sqrt{\frac{F}{u} }[/tex]
u is mass/length and F is tension
F(tension)=m*g
F=(0.00055)*(9.8)
F=[tex]5.39*10^{-3}N\\ Volume=pi*d^{2}*L\\ Volume=(3.14)*(2*10^{-6} )^{2}*(1.2)\\ Volume=1.5072*10^{-11}m^{3}[/tex]
[tex]mass=desnsity*volume\\m=1300*(1.5072*10^{-11}) \\m=1.959*10^{-8}kg\\[/tex]
Mass per length(u) is given as
[tex]u=\frac{1.959*10^{-8} }{1.2} \\u=1.6328*10^{-8}\frac{kg}{m}[/tex]
[tex]V=\sqrt{\frac{F}{u} }\\ V=\sqrt{\frac{5.39*10^{-3} }{1.6328*10^{-8} } } \\V=574.55 \frac{m}{s}[/tex]
and for 1.2m length time is
[tex]t=L/V\\t=\frac{1.2}{574.55}[/tex]
so the answer is
[tex]t=2.08*10^{-3}seconds\\ t=2.08 milliseconds[/tex]
