Answer: C = Q/4πR
Explanation:
Volume(V) of a sphere = 4πr^3
Charge within a small volume 'dV' is given by:
dq = ρ(r)dV
ρ(r) = C/r^2
Volume(V) of a sphere = 4/3(πr^3)
dV/dr = (4/3)×3πr^2
dV = 4πr^2dr
Therefore,
dq = ρ(r)dV ; dq =ρ(r)4πr^2dr
dq = C/r^2[4πr^2dr]
dq = 4Cπdr
FOR TOTAL CHANGE 'Q', we integrate dq
∫dq = ∫4Cπdr at r = R and r = 0
∫4Cπdr = 4Cπr
Q = 4Cπ(R - 0)
Q = 4CπR - 0
Q = 4CπR
C = Q/4πR
The value of C in terms of Q and R is [Q/4πR]
Answer:
H=1020.12m
Explanation:
From a balance of energy:
where H is the height it reached, d is the distance it traveled along the ramp and Ff = μk*N.
The relation between H and d is given by:
H = d*sin(30) Replace this into our previous equation:

From a sum of forces:
N -mg*cos(30) = 0 => N = mg*cos(30) Replacing this:
Now we can solve for d:
d = 2040.23m
Thus H = 1020.12m
Answer:

Explanation:
Since work done is in the form of potential energy, we will use the formula of potential energy here.
We know that,
<h3>P.E. = mgh </h3>
Where,
m = mass = 20 kg
g = acceleration due to gravity = 10 m/s²
h = vertical height = 20 m
So,
<h3>Work done = mgh</h3>
Work done = (20)(10)(20)
Work done = 4000 joules
Work done = 4 kJ
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