Answer:
U = 1 / r²
Explanation:
In this exercise they do not ask for potential energy giving the expression of force, since these two quantities are related
F = - dU / dr
this derivative is a gradient, that is, a directional derivative, so we must have
dU = - F. dr
the esxresion for strength is
F = B / r³
let's replace
∫ dU = - ∫ B / r³ dr
in this case the force and the displacement are parallel, therefore the scalar product is reduced to the algebraic product
let's evaluate the integrals
U - Uo = -B (- / 2r² + 1 / 2r₀²)
To complete the calculation we must fix the energy at a point, in general the most common choice is to make the potential energy zero (Uo = 0) for when the distance is infinite (r = ∞)
U = B / 2r²
we substitute the value of B = 2
U = 1 / r²
Answer:
D = -4/7 = - 0.57
C = 17/7 = 2.43
Explanation:
We have the following two equations:

First, we isolate C from equation (2):

using this value of C from equation (3) in equation (1):

<u>D = - 0.57</u>
Put this value in equation (3), we get:

<u>C = 2.43</u>
Answer:
0.369 V
<u>Explanation:</u>
Given :
Capacitance ( c ) = 650 × 10–4 F
Charge ( q ) = 24 × 10–3 C
We are asked to find potential difference ( v )!
We know:
q = c v
= > v = q / c
Putting values here we get:
= > v = ( 24 × 10–3 ) / ( 650 × 10–4 ) V
= > v = 240 / 650 V
= > v = 24 / 65 V
= > v = 0.369 V
Therefore, potential difference between the plates is 0.369 V
Angular frequency of pendulum is given by

for both pendulum we have


For other pendulum


now we have relate angular frequency given as
[tex\omega_1 - \omega_2 = 3.13 - 2.98 = 0.15 rad/s[/tex]
now time taken to become in phase again is given as


now number of oscillations complete in above time


