From the definition of apparent magnitude, we know that:
where:
m = apparent magnitude
F = corresponding flux
We also know that the flux is given by the formula:
where:
L = luminosity
d = distance
Therefore:
Now, let's apply these formulae to the same star (therefore, same luminosity), using apparent magnitude and absolute magnitude (which is defined as the apparent magnitude the star would have if it were at a distance of 10pc):
Now, let's solve for m:
= <span>
</span>
= 13
Hence,
the apparent magnitude of the star would be m = +13
Change in electric potential energy: 121.5 nJ
Explanation:
For a charged particle moving in an electric field, the change in electric potential energy of the particle is given by
where:
q is the charge of the particle
is the potential difference between the initial and final position of the particle
For the point charge in this problem, we have:
is the charge
is the potential difference
Therefore, the change in electric potential energy is
Learn more about electric fields:
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B.
This equation quantifies the inter convertibility of mass and energy and helps us understand the large amount of energy that would be released if mass were converted to energy.<span />
Answer:
Explanation:
The problem is related to rotational motion . So we shall find out rotational kinetic energy .
K E = 1/2 x I ω²
ω is the final angular velocity
Moment of inertial of the disk
I ₁ = 1/2 m r²
= .5 x 165 x 2.93²
= 708.25 kgm²
Moment of inertial of the person
I₂ = mr²
= 62.5 x 2.93²
= 536.55 kgm²
ω₂ = v / R
= 3.11 / 2.93 rad /s
At the time of jumping , law of conservation of angular momentum will apply
I₁ ω₁ + I₂ω₂ = (I₁ + I₂)ω
708.25 x0.691 + 536.55 x ( 3.11 / 2.93 ) = ( 708.25 + 536.55 ) ω
ω = 0 .85 rad/ s
K E = 1/2 x I ω²
= .5 x ( 708.25 + 536.55 ) ( .85 )²
449.68 J