Answer:
5.82812 rad/s
Explanation:
L = Length of meter stick = 1 m = 100 cm
= The center of mass of the stick = ![\frac{L}{2}-0.22=0.5-0.22=0.28\ m](https://tex.z-dn.net/?f=%5Cfrac%7BL%7D%7B2%7D-0.22%3D0.5-0.22%3D0.28%5C%20m)
= Angular velocity
Moment of inertia of the system is given by
![I=I_c+mr^2\\\Rightarrow I=\frac{mL^2}{12}+mr^2\\\Rightarrow I=\frac{m1^2}{12}+m0.28^2\\\Rightarrow I=m(\frac{1}{12}+0.0784)](https://tex.z-dn.net/?f=I%3DI_c%2Bmr%5E2%5C%5C%5CRightarrow%20I%3D%5Cfrac%7BmL%5E2%7D%7B12%7D%2Bmr%5E2%5C%5C%5CRightarrow%20I%3D%5Cfrac%7Bm1%5E2%7D%7B12%7D%2Bm0.28%5E2%5C%5C%5CRightarrow%20I%3Dm%28%5Cfrac%7B1%7D%7B12%7D%2B0.0784%29)
As the energy in the system is conserved
![mgh=I\frac{\omega^2}{2}\\\Rightarrow mgh=m(\frac{1}{12}+0.0784)\frac{\omega^2}{2}\\\Rightarrow gh=(\frac{1}{12}+0.0784)\frac{\omega^2}{2}\\\Rightarrow \omega=\sqrt{\frac{2gh}{\frac{1}{12}+0.0784}}\\\Rightarrow \omega=\sqrt{\frac{2\times 9.81\times 0.28}{\frac{1}{12}+0.0784}}\\\Rightarrow \omega=5.82812\ rad/s](https://tex.z-dn.net/?f=mgh%3DI%5Cfrac%7B%5Comega%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20mgh%3Dm%28%5Cfrac%7B1%7D%7B12%7D%2B0.0784%29%5Cfrac%7B%5Comega%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20gh%3D%28%5Cfrac%7B1%7D%7B12%7D%2B0.0784%29%5Cfrac%7B%5Comega%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20%5Comega%3D%5Csqrt%7B%5Cfrac%7B2gh%7D%7B%5Cfrac%7B1%7D%7B12%7D%2B0.0784%7D%7D%5C%5C%5CRightarrow%20%5Comega%3D%5Csqrt%7B%5Cfrac%7B2%5Ctimes%209.81%5Ctimes%200.28%7D%7B%5Cfrac%7B1%7D%7B12%7D%2B0.0784%7D%7D%5C%5C%5CRightarrow%20%5Comega%3D5.82812%5C%20rad%2Fs)
The maximum angular velocity is 5.82812 rad/s
Answer:
coal tar is one of the product of coal
Answer:
F = 614913.88 N
Explanation:
We are given;
Mass of pile driver; m = 1800 kg
Height of fall of pole driver; h = 4.6 m
Depth driven into beam; d = 13.6 cm = 0.136 m
Now, from energy equations and applying to this question, we can write that;
Workdone = Change in potential energy
Formula for workdone is; W = F × d
While the average potential energy here is; W = mg(h + d)
Thus;
Fd = mg(h + d)
Where F is the average force exerted by the beam on the pile driver while in bringing it to rest.
Making F the subject, we have;
F = mg(h + d)/d
F = 1800 × 9.81 × (4.6 + 0.136)/0.136
F = 614913.88 N
Answer:
λ₁ = 2.50 10⁻² m, λ₂ = 1.66 10⁻² m
Explanation:
Microwave communication is very efficient because it does not have atmospheric interference, for which it is widely used and has been regulated to avoid interference, the ku band is in the range between 12 and 18 GHz.
Let's calculate the wavelength for the two extreme frequencies of this band
wavelength and frequency are related
c = λ f
λ = c / f
f₁ = 12 GHz = 12 10⁹ Hz
λ₁ = 3 10⁸ /12 10⁹
λ₁ = 2.50 10⁻² m
f₂ = 18 GHz = 18 10⁹ Hz
λ₂ = 3 10⁸ /18 10⁹
λ₂ = 1.66 10⁻² m
Unfortunately in your exercise the specific frequency is not fired, for significant figures they must be the same number as the figures of the frequency, in general the frequency has 3 or 4 significant figures
Answer:
first lens v = 48 cm
second lens v = -15.6 cm
magnification = 1.67
final image is virtual
and final image is upright
Explanation:
given data
distance = 16 cm
focal length f1 = 12 cm
focal length f2 = 10.0 cm
to find out
location of the final image and magnification and Type of image
solution
we apply here lens formula that is
1/f = 1/v + 1/u .....................1
put here all value and find v for 1st lens
1/12 = 1/v + 1/16
v = 48 cm
and find v for 2nd lens
here u = 20- 48 = -28
- 1/10 = 1/v - 1/28
v = -15.6 cm
and
magnification = first lens (v/u) × second lens ( v/u)
magnification = (-15.6/-28) × ( 48/16)
magnification = 1.67
so here final image is virtual
and final image is upright