7 I think, I’m sorry if I’m wrong
Answer:
correct option is C) 2.8
Step-by-step explanation:
given data
string vibrates form = 8 loops
in water loop formed = 10 loops
solution
we consider mass of stone = m
string length = l
frequency of tuning = f
volume = v
density of stone =
case (1)
when 8 loop form with 2 adjacent node is
so here
..............1
![l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}](https://tex.z-dn.net/?f=l%20%3D%204%20%5Clambda_1%5C%5C%5C%5C%5Clambda_1%20%3D%20%5Cfrac%7Bl%7D%7B4%7D)
and we know velocity is express as
velocity = frequency × wavelength .....................2
= f ×
here tension = mg
so
= f ×
..........................3
and
case (2)
when 8 loop form with 2 adjacent node is
..............4
![l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}](https://tex.z-dn.net/?f=l%20%3D%205%20%5Clambda_1%5C%5C%5C%5C%5Clambda_1%20%3D%20%5Cfrac%7Bl%7D%7B5%7D)
when block is immersed
equilibrium eq will be
Tenion + force of buoyancy = mg
T + v ×
× g = mg
and
T = v ×
- v ×
× g
from equation 2
f ×
= f ×
.......................5
now we divide eq 5 by the eq 3
![\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bvg%20%28%5Crho%20_%7Bstone%7D%20-%20%5Crho%20_%7Bwater%7D%29%7D%7B%5Cmu%20vg%20%5Ctimes%20%5Crho%20_%7Bstone%7D%7D%7D%20%3D%20%5Cfrac%7Bfl%7D%7B5%7D%20%5Ctimes%20%5Cfrac%7B4%7D%7Bfl%7D)
solve irt we get
![1 - \frac{\rho _{stone}}{\rho _{water}} = \frac{16}{25}](https://tex.z-dn.net/?f=1%20-%20%5Cfrac%7B%5Crho%20_%7Bstone%7D%7D%7B%5Crho%20_%7Bwater%7D%7D%20%20%3D%20%5Cfrac%7B16%7D%7B25%7D)
so
relative density ![\frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Crho%20_%7Bstone%7D%7D%7B%5Crho%20_%7Bwater%7D%7D%20%3D%20%5Cfrac%7B25%7D%7B9%7D)
relative density = 2.78 ≈ 2.8
so correct option is C) 2.8
The Numerator is 1, which is the top. The Denominator is the 8. I like to remember (D)own is the (D)enominator.
A planet's day is the time it takes the planet to rotate or spin once on its axis. Saturn rotates faster than Earth so a day on Saturn is shorter than a day on Earth. A day on Saturn is 10.656<span> hours long while a day on Earth is </span>23.934<span> hours long.</span><span />