Answer:
See the explanation below
Explanation:
Density is defined as the relationship between mass and volume, i.e. the following equation can be used:
density = m/v
where:
density [kg/m^3]
m = mass [kg]
v = volume [m^3]
If we change the volume of a body by reducing its size, its mass will also decrease proportionally with a density as seen in the equation.
m = density*v
To understand this concept more clearly, let's use the following example:
We know that the density of water is equal to 1000 [kg/m^3], that is, 1 cubic meter of water contains 1000 kilograms of water, using the equation.
1000 = m /1
m = 1000*1 = 1000 [kg]
Now if we have 500 kilograms of water, that would pass with the volume so that the density remains constant.
1000 = 500/v
v = 500/1000
v = 0.5 [m^3]
We can see that the volume of water has halved. Since the mass of water was reduced by half. That is, the relationship between mass and volume is proportional to the density of the material or substance.
Answer:
The frequency is
Explanation:
From the question we are told that
The frequency of the tuning fork is ![f_t = 440 \ Hz](https://tex.z-dn.net/?f=f_t%20%20%3D%20%20440%20%5C%20Hz)
The beat period is ![T = 2 \ s](https://tex.z-dn.net/?f=T%20%20%3D%20%202%20%5C%20%20s)
Generally the beat frequency is mathematically represented as
![f_b = \frac{1}{2}](https://tex.z-dn.net/?f=f_b%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D)
![f_b = 0.5 \ Hz](https://tex.z-dn.net/?f=f_b%20%20%3D%200.5%20%5C%20%20Hz)
The beat frequency is also represented mathematically as
![f_b = f_t - f](https://tex.z-dn.net/?f=f_b%20%20%3D%20%20f_t%20%20-%20%20f)
Where
is the frequency of the piano
So
Answer with Explanation:
We are given that
Mass of squirrel,m=530 g=![\frac{530}{1000}=0.530 kg](https://tex.z-dn.net/?f=%5Cfrac%7B530%7D%7B1000%7D%3D0.530%20kg)
1kg=1000 g
Area=A=![935 cm^2=935\times 10^{-4} m^2](https://tex.z-dn.net/?f=935%20cm%5E2%3D935%5Ctimes%2010%5E%7B-4%7D%20m%5E2)
![1 cm^2=10^{-4} m^2](https://tex.z-dn.net/?f=1%20cm%5E2%3D10%5E%7B-4%7D%20m%5E2)
Height,h=4.4 m
C=1
![\rho=1.21 kg/m^3](https://tex.z-dn.net/?f=%5Crho%3D1.21%20kg%2Fm%5E3)
Width of rectangular prism,b=11.6 cm=![\frac{11.6}{100}=0.116 m](https://tex.z-dn.net/?f=%5Cfrac%7B11.6%7D%7B100%7D%3D0.116%20m)
1 m=100 cm
Length,l=23.2 cm=![0.232 m](https://tex.z-dn.net/?f=0.232%20m)
Area=![l\times b=0.116\times 0.232=0.0269 m^2](https://tex.z-dn.net/?f=l%5Ctimes%20b%3D0.116%5Ctimes%200.232%3D0.0269%20m%5E2)
Terminal velocity,![v_t=\sqrt{\frac{2mg}{\rho CA}}](https://tex.z-dn.net/?f=v_t%3D%5Csqrt%7B%5Cfrac%7B2mg%7D%7B%5Crho%20CA%7D%7D)
Where ![g=9.8 m/s^2](https://tex.z-dn.net/?f=g%3D9.8%20m%2Fs%5E2)
Using the formula
![v_t=\sqrt{\frac{2\times 0.530\times 9.8}{1.21\times 1\times 0.0269}}](https://tex.z-dn.net/?f=v_t%3D%5Csqrt%7B%5Cfrac%7B2%5Ctimes%200.530%5Ctimes%209.8%7D%7B1.21%5Ctimes%201%5Ctimes%200.0269%7D%7D)
![v_t=17.86 m/s](https://tex.z-dn.net/?f=v_t%3D17.86%20m%2Fs)
The velocity of person,![v=\sqrt{2gh}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B2gh%7D)
Using the formula
![v=\sqrt{2\times 9.8\times 4.4}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B2%5Ctimes%209.8%5Ctimes%204.4%7D)
![v=9.29 m/s](https://tex.z-dn.net/?f=v%3D9.29%20m%2Fs)
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