Answer:
1.54 s
Explanation:
Considering that the legs constitute 16% of the total weight of the man then mass, ![m= \frac {16}{100}\times 67=10.72 Kg](https://tex.z-dn.net/?f=m%3D%20%5Cfrac%20%7B16%7D%7B100%7D%5Ctimes%2067%3D10.72%20Kg)
The legs also constitute 48% of his height hence ![H=\frac {48}{100}\times 1.83=0.8784 m](https://tex.z-dn.net/?f=H%3D%5Cfrac%20%7B48%7D%7B100%7D%5Ctimes%201.83%3D0.8784%20m)
The moment of inertia of a cylinder rotating about a perpendicular axis at one end is
hence ![I=\frac {10.72\times 0.8784^{2}}{3}=2.757135974Kg.m^{2}](https://tex.z-dn.net/?f=I%3D%5Cfrac%20%7B10.72%5Ctimes%200.8784%5E%7B2%7D%7D%7B3%7D%3D2.757135974Kg.m%5E%7B2%7D)
We also know that the period is given by ![2\pi \sqrt{\frac {I}{mgh}}](https://tex.z-dn.net/?f=2%5Cpi%20%5Csqrt%7B%5Cfrac%20%7BI%7D%7Bmgh%7D%7D)
Here, h=0.5H= 0.5*0.8784=0.4392 m
Taking g as 9.81 kg/m2 then
![T= 2\pi \sqrt{\frac {2.757135974}{10.72\times 9.81\times 0.4392}}\\=1.535132615 s\\\boxed{\approx 1.54 s}](https://tex.z-dn.net/?f=T%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%20%7B2.757135974%7D%7B10.72%5Ctimes%209.81%5Ctimes%200.4392%7D%7D%5C%5C%3D1.535132615%20s%5C%5C%5Cboxed%7B%5Capprox%201.54%20s%7D)
Answer:
f = 7.97 x 10⁶ Hz = 7.97 MHz
Explanation:
The speed of a wave is given by the following formula:
![v = f\lambda](https://tex.z-dn.net/?f=v%20%3D%20f%5Clambda)
where,
v = speed of the ultrasound wave through human tissue = 1540 m/s
f = frequency of ultrasound wave required = ?
λ = wavelength of ultrasound waves = smallest detail required = 0.193 mm
λ = 0.193 mm = 1.93 x 10⁻⁴ m
Therefore,
<u>f = 7.97 x 10⁶ Hz = 7.97 MHz</u>
Answer:
The magnetic field of a magnet any magnet is stronger at the poles, so the poles have a bigger magnetic field which types: bar magnetics and etc.hope this helps
Answer:
![\theta = n\pi/2, {\rm where~n~is~an~integer.}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20n%5Cpi%2F2%2C%20%7B%5Crm%20where~n~is~an~integer.%7D)
Explanation:
We should first find the velocity and acceleration functions. The velocity function is the derivative of the position function with respect to time, and the acceleration function is the derivative of the velocity function with respect to time.
![\vec{v}(t) = \frac{d\vec{r}(t)}{dt} = (2)\^i + (\sqrt{7})\^j + (6t)\^k](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%28t%29%20%3D%20%5Cfrac%7Bd%5Cvec%7Br%7D%28t%29%7D%7Bdt%7D%20%3D%20%282%29%5C%5Ei%20%2B%20%28%5Csqrt%7B7%7D%29%5C%5Ej%20%2B%20%286t%29%5C%5Ek)
Similarly,
![\vec{a}(t) = \frac{d\vec{v}(t)}{dt} = (6)\^k](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%28t%29%20%3D%20%5Cfrac%7Bd%5Cvec%7Bv%7D%28t%29%7D%7Bdt%7D%20%3D%20%286%29%5C%5Ek)
Now, the angle between velocity and acceleration vectors can be found.
The angle between any two vectors can be found by scalar product of them:
![\vec{A}.\vec{B} = |\vec{A}|.|\vec{B}|.\cos(\theta)](https://tex.z-dn.net/?f=%5Cvec%7BA%7D.%5Cvec%7BB%7D%20%3D%20%7C%5Cvec%7BA%7D%7C.%7C%5Cvec%7BB%7D%7C.%5Ccos%28%5Ctheta%29)
So,
![\vec{v}(t).\vec{a}(t) = |\vec{v}(t)|.|\vec{a}(t)|.\cos(\theta)\\36t = \sqrt{4 + 7 + 36t^2}.6.\cos(\theta)](https://tex.z-dn.net/?f=%5Cvec%7Bv%7D%28t%29.%5Cvec%7Ba%7D%28t%29%20%3D%20%7C%5Cvec%7Bv%7D%28t%29%7C.%7C%5Cvec%7Ba%7D%28t%29%7C.%5Ccos%28%5Ctheta%29%5C%5C36t%20%3D%20%5Csqrt%7B4%20%2B%207%20%2B%2036t%5E2%7D.6.%5Ccos%28%5Ctheta%29)
At time t = 0, this equation becomes
![0 = 6\sqrt{11}\cos(\theta)\\\cos(\theta) = 0\\\theta = n\pi/2, {\rm where~n~is~an~integer.}](https://tex.z-dn.net/?f=0%20%3D%206%5Csqrt%7B11%7D%5Ccos%28%5Ctheta%29%5C%5C%5Ccos%28%5Ctheta%29%20%3D%200%5C%5C%5Ctheta%20%3D%20n%5Cpi%2F2%2C%20%7B%5Crm%20where~n~is~an~integer.%7D)
Answer:
Neutral atom means the number of protons is equal to the number of electrons.
Explanation: