Answer:
k = 2.279
Explanation:
Given:
Magnitude of charge on each plate, Q = 172 μC
Now,
the capacitance, C of a capacitor is given as:
C = Q/V
where,
V is the potential difference
Thus, the capacitance due to the charge of 172 μC will be
C = ![\frac{(172\ \mu C)}{V}](https://tex.z-dn.net/?f=%5Cfrac%7B%28172%5C%20%5Cmu%20C%29%7D%7BV%7D)
Now, when the when the additional charge is accumulated
the capacitance (C') will be
C' = ![\frac{(172+220)\ \mu C)}{V}](https://tex.z-dn.net/?f=%5Cfrac%7B%28172%2B220%29%5C%20%5Cmu%20C%29%7D%7BV%7D)
or
C' = ![\frac{(392)\ \mu C)}{V}](https://tex.z-dn.net/?f=%5Cfrac%7B%28392%29%5C%20%5Cmu%20C%29%7D%7BV%7D)
now the dielectric constant (k) is given as:
![k=\frac{C'}{C}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BC%27%7D%7BC%7D)
substituting the values, we get
![k=\frac{\frac{(392\ \mu C)}{V}}{\frac{(172)\ \mu C)}{V}}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B%5Cfrac%7B%28392%5C%20%5Cmu%20C%29%7D%7BV%7D%7D%7B%5Cfrac%7B%28172%29%5C%20%5Cmu%20C%29%7D%7BV%7D%7D)
or
k = 2.279
4. The Coyote has an initial position vector of
.
4a. The Coyote has an initial velocity vector of
. His position at time
is given by the vector
![\vec r=\vec r_0+\vec v_0t+\dfrac12\vec at^2](https://tex.z-dn.net/?f=%5Cvec%20r%3D%5Cvec%20r_0%2B%5Cvec%20v_0t%2B%5Cdfrac12%5Cvec%20at%5E2)
where
is the Coyote's acceleration vector at time
. He experiences acceleration only in the downward direction because of gravity, and in particular
where
. Splitting up the position vector into components, we have
with
![r_x=\left(3.5\,\dfrac{\mathrm m}{\mathrm s}\right)t](https://tex.z-dn.net/?f=r_x%3D%5Cleft%283.5%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%5Cright%29t)
![r_y=15.5\,\mathrm m-\dfrac g2t^2](https://tex.z-dn.net/?f=r_y%3D15.5%5C%2C%5Cmathrm%20m-%5Cdfrac%20g2t%5E2)
The Coyote hits the ground when
:
![15.5\,\mathrm m-\dfrac g2t^2=0\implies t=1.8\,\mathrm s](https://tex.z-dn.net/?f=15.5%5C%2C%5Cmathrm%20m-%5Cdfrac%20g2t%5E2%3D0%5Cimplies%20t%3D1.8%5C%2C%5Cmathrm%20s)
4b. Here we evaluate
at the time found in (4a).
![r_x=\left(3.5\,\dfrac{\mathrm m}{\mathrm s}\right)(1.8\,\mathrm s)=6.3\,\mathrm m](https://tex.z-dn.net/?f=r_x%3D%5Cleft%283.5%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%5Cright%29%281.8%5C%2C%5Cmathrm%20s%29%3D6.3%5C%2C%5Cmathrm%20m)
5. The shell has initial position vector
, and we're told that after some time the bullet (now separated from the shell) has a position of
.
5a. The vertical component of the shell's position vector is
![r_y=1.52\,\mathrm m-\dfrac g2t^2](https://tex.z-dn.net/?f=r_y%3D1.52%5C%2C%5Cmathrm%20m-%5Cdfrac%20g2t%5E2)
We find the shell hits the ground at
![1.52\,\mathrm m-\dfrac g2t^2=0\implies t=0.56\,\mathrm s](https://tex.z-dn.net/?f=1.52%5C%2C%5Cmathrm%20m-%5Cdfrac%20g2t%5E2%3D0%5Cimplies%20t%3D0.56%5C%2C%5Cmathrm%20s)
5b. The horizontal component of the bullet's position vector is
![r_x=v_0t](https://tex.z-dn.net/?f=r_x%3Dv_0t)
where
is the muzzle velocity of the bullet. It traveled 3500 m in the time it took the shell to fall to the ground, so we can solve for
:
![3500\,\mathrm m=v_0(0.56\,\mathrm s)\implies v_0=6300\,\dfrac{\mathrm m}{\mathrm s}](https://tex.z-dn.net/?f=3500%5C%2C%5Cmathrm%20m%3Dv_0%280.56%5C%2C%5Cmathrm%20s%29%5Cimplies%20v_0%3D6300%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D)
Answer:
The correct option is (d).
Explanation:
- The energy a particle has because of its charge and its position relative to another particle is called thermal energy.
- It is the energy that comes from heat. This is generated by the movement of the particles in an object.
- Thermal energy is the energy an object or system has due to the movement of particles within.
Hence, the correct option is (d).
Answer:
D. Asthenosphere
Explanation:
The asthenosphere is relatively plastic part of the mantle which underlies the brittle lithosphere. In the asthenosphere, it is generally believed that the rocks are in ductile state and easily moves. It is the site of convection within the earth. In mantle convection, hot and light materials rises and keeps moving into upper crustal levels till they solidify. Here also, cold and denser materials sinks deeper till they turn to melt. This differences in temperature and density sets up a convective cell within the mantle. Several convective cells are in the mantle.
Explanation:
I think the third one coz it's so good