Answer:
Explanation:
The volume of a sphere is:
V = 4/3 * π * a^3
The volume charge density would then be:
p = Q/V
p = 3*Q/(4 * π * a^3)
If the charge density depends on the radius:
p = f(r) = k * r
I integrate the charge density in spherical coordinates. The charge density integrated in the whole volume is equal to total charge.





Since p = k*r
Q = p*π^2*r^3 / 2
Then:
p(r) = 2*Q / (π^2*r^3)
The spring has a spring constant of 1.00 * 10^3 N/m and the mass has been displaced 20.0 cm then the restoring force is 20000 N/m.
Explanation:
When a spring is stretched or compressed its length changes by an amount x from its equilibrium length then the restoring force is exerted.
spring constant is k = 1.00 * 10^3 N/m
mass is x = 20.0 cm
According to Hooke's law, To find restoring force,
F = - kx
= - 1.00 *10 ^3 * 20.0
F = 20000 N/m
Thus, the spring has a spring constant of 1.00 * 10^3 N/m and the mass has been displaced 20.0 cm then the restoring force is 20000 N/m.
During the fall, all the initial potential energy of the rock

has converted into kinetic energy of motion

where h is the initial height of the rock, m its mass, and v its velocity just before hitting the water. So, for energy conservation, we have

and so we can find the value of K, the kinetic energy of the rock just before hitting the ground: