E = ½KA^2 is the mechanical energy of any oscillator. It is the sum of elastic potential energy and
kinetic energy. When amplitude A
decreases by 3%, then
(E2-E1)/E1 = {½K(A2^2/A1^2) }/ ½K(A1^2)
= {(A2^2 – A1^2) / (A1^2)}
= 97^2 – 100^2/100^2
= 5.91% of the mechanical energy is lost each cycle.
Answer:
Explanation:
We have the following relation between power, P and intensity, I

= 
= 
We also have the following relationship between electric field and electromagnetic radiation thus

Hence 
substituting the values of I, c and e, we have

The density of the substance is<u> 10.5 g/cm³.</u>
The jewelry is made out of <u>Silver.</u>
Density ρ is defined as the ratio of mass <em>m</em> of the substance to its volume V<em>. </em> The cylinder contains a volume <em>V₁ of water</em> and when the jewelry is immersed in it, the total volume of water and the jewelry is found to be V₂.
The volume <em>V</em> of the jewelry is given by,

Substitute 48.6 ml for <em>V₁ </em>and 61.2 ml for V₂.

calculate the density ρ of the jewelry using the expression,

Substitute 132.6 g for <em>m</em> and 12.6 ml for <em>V</em>.

Since
,
The density of the jewelry is <u> 10.5 g/cm³.</u>
From standard tables, it can be seen that the substance used to make the jewelry is <u>silver</u><em><u>, </u></em>which has a density 10.5 g/cm³.
In triangle ABC , using Pythagorean theorem
BC = sqrt(AB² + AC²)
r = sqrt(y² + x²) eq-1
taking derivative both side relative to "t"
dr/dt = (1/(2 sqrt(y² + x²) ) ) (2 y (dy/dt) + 2 x (dx/dt))
dr/dt = (1/(2 sqrt(0.5² + 0.5²) ) ) (2 (0.5) (dy/dt) + 2 (0.5) (dx/dt))
dr/dt = (1/(2 sqrt(0.5² + 0.5²) ) ) ( v₁ + v₂)
15= (1/(2 sqrt(0.5² + 0.5²) ) ) ( - 30 + v₂)
v₂ = 51.2 m/s
Answer:

Explanation:
Let the total charge on the big drop is given as Q
now if the radius of the drop is R then electric potential of the big drop is given as

Now if it break into n identical drops
then let the charge on each drop is "q" and radius is "r"
by volume conservation


now we have potential of smaller drop given as



