Answer:
Explanation:
λ(x) = λo x/ L
(a) The total charge is Q.
![Q=\int_{0}^{L}dq](https://tex.z-dn.net/?f=Q%3D%5Cint_%7B0%7D%5E%7BL%7Ddq)
![Q=\int_{0}^{L}\frac{\lambda _{0}x}{L}dx](https://tex.z-dn.net/?f=Q%3D%5Cint_%7B0%7D%5E%7BL%7D%5Cfrac%7B%5Clambda%20_%7B0%7Dx%7D%7BL%7Ddx)
![Q=\frac{\lambda _{0}}{2L}\left ( x^{2} \right )_{0}^{L}](https://tex.z-dn.net/?f=Q%3D%5Cfrac%7B%5Clambda%20_%7B0%7D%7D%7B2L%7D%5Cleft%20%28%20x%5E%7B2%7D%20%5Cright%20%29_%7B0%7D%5E%7BL%7D)
![Q=\frac{\lambda _{0}}{2L}](https://tex.z-dn.net/?f=Q%3D%5Cfrac%7B%5Clambda%20_%7B0%7D%7D%7B2L%7D)
λo = 2Q/L
(b)
Let at a distance x from the origin the charge is dq.
so, dq = (2Q/L) x/ L dx
![dq=\frac{2Qx}{L^{2}}dx](https://tex.z-dn.net/?f=dq%3D%5Cfrac%7B2Qx%7D%7BL%5E%7B2%7D%7Ddx)
The potential due to this small charge at a distance d to the left of origin
![dV = \frac{KdQ}{d+x}](https://tex.z-dn.net/?f=dV%20%3D%20%5Cfrac%7BKdQ%7D%7Bd%2Bx%7D)
![\int_{0}^{V}dV = \frac{2KQ}{L^{2}}\int_{0}^{L}\frac{xdx}{d+x}](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7BV%7DdV%20%3D%20%5Cfrac%7B2KQ%7D%7BL%5E%7B2%7D%7D%5Cint_%7B0%7D%5E%7BL%7D%5Cfrac%7Bxdx%7D%7Bd%2Bx%7D)
![V = \frac{2KQ}{L^{2}}\int_{0}^{L}\left ( 1- \frac{d}{d+x}\right )dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B2KQ%7D%7BL%5E%7B2%7D%7D%5Cint_%7B0%7D%5E%7BL%7D%5Cleft%20%28%201-%20%5Cfrac%7Bd%7D%7Bd%2Bx%7D%5Cright%20%29dx)
![V = \frac{2KQ}{L^{2}}\times \left ( x-dln(d+x) \right )\int_{0}^{L}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B2KQ%7D%7BL%5E%7B2%7D%7D%5Ctimes%20%5Cleft%20%28%20x-dln%28d%2Bx%29%20%5Cright%20%29%5Cint_%7B0%7D%5E%7BL%7D)
![V = \frac{2KQ}{L^{2}}\times \left ( L-dln(d+L)-0+dlnd \right )](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B2KQ%7D%7BL%5E%7B2%7D%7D%5Ctimes%20%5Cleft%20%28%20L-dln%28d%2BL%29-0%2Bdlnd%20%5Cright%20%29)
![V = \frac{Q}{4\pi \epsilon _{0}L^{2}}\times \left ( L+d\times ln\left (\frac{d}{d+L} \right )\right )](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7BQ%7D%7B4%5Cpi%20%5Cepsilon%20_%7B0%7DL%5E%7B2%7D%7D%5Ctimes%20%5Cleft%20%28%20L%2Bd%5Ctimes%20ln%5Cleft%20%28%5Cfrac%7Bd%7D%7Bd%2BL%7D%20%20%5Cright%20%29%5Cright%20%29)
Answer:
first
Explanation:
also wat u need help with
Answer:
the resulting angular speed after she pulls her hand inwards in (rad/s) is 27.02 rad/s
Explanation:
Given that :
the initial angular speed ![\omega_1 = 1.9 \ \ rev/s](https://tex.z-dn.net/?f=%5Comega_1%20%3D%201.9%20%5C%20%5C%20rev%2Fs)
Initial rotational inertia ![I_1 = 12.00 \ \ kg.m^2](https://tex.z-dn.net/?f=I_1%20%3D%2012.00%20%5C%20%5C%20kg.m%5E2)
Final angular speed ![\omega_2 = ???](https://tex.z-dn.net/?f=%5Comega_2%20%3D%20%3F%3F%3F)
Final rotational inertia ![I_2 = 5.3 \ \ kg.m^2](https://tex.z-dn.net/?f=I_2%20%3D%205.3%20%5C%20%5C%20kg.m%5E2)
According to conservation of momentum :
Initial momentum = final momentum
![I_1 \omega_1 = I_2 \omega_2](https://tex.z-dn.net/?f=I_1%20%5Comega_1%20%3D%20I_2%20%5Comega_2)
![\omega_2 = \frac{I_1 \omega_1}{I_2}](https://tex.z-dn.net/?f=%5Comega_2%20%3D%20%5Cfrac%7BI_1%20%5Comega_1%7D%7BI_2%7D)
![\omega_2 = \frac{12.00*1.9}{5.3}](https://tex.z-dn.net/?f=%5Comega_2%20%3D%20%5Cfrac%7B12.00%2A1.9%7D%7B5.3%7D)
![rev/s](https://tex.z-dn.net/?f=rev%2Fs)
To rad/s ; we have:
![1 \ rev/s = 2 \pi \ \ rad/s](https://tex.z-dn.net/?f=1%20%20%5C%20%20%20rev%2Fs%20%3D%202%20%5Cpi%20%5C%20%5C%20%20rad%2Fs)
![\omega_2 = 4.3 * 2 \pi \ \ rad/s](https://tex.z-dn.net/?f=%5Comega_2%20%3D%204.3%20%2A%202%20%5Cpi%20%5C%20%5C%20%20rad%2Fs)
![\omega_2 = 27.02 \ \ rad/s](https://tex.z-dn.net/?f=%5Comega_2%20%3D%2027.02%20%20%5C%20%5C%20rad%2Fs)
Therefore the resulting angular speed after she pulls her hand inwards in (rad/s) = 27.02 rad/s
Answer:
C. One liter of water
Explanation:
One liter of water is closest to 1 kilogram. The other options don't make sense because a dime cannot be close to a mass of 1 kilogram, neither an average size banana or an average person
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Answer: Hope this helps!
Explanation:
a rock formed from particles that are deposited and lithified are sedimentary.
rocks formed from cooling and hardening magma or lava is igneous.
a rock formed when an already existing rock is subjected to extreme heat and pressure is metamorphic.