Answer:
The value of R is
.
(B) is correct option.
Explanation:
Given that,
In analyzing distances by apply ing the physics of gravitational forces, an astronomer has obtained the expression

We need to calculate this for value of R


So, The nearest option of the value of R is 
Hence, The value of R is
.
Answer:
The amplitude of the eardrum's oscillation is 6.65×10^-13 m.
Explanation:
Given data:
The sound has a frequency of 262 Hz
The sound level is 84 dB
The air density is 1.21 kg/m^3
The speed of sound is 346 m/s
Solution:
As, Intensity of sound is given by,
I = Io×10^(s/10 db)
I = 2×π^2×ρ×v×f^2×Sm^2
Thus,
Sm = √(Io×10^(s/10 db)) / √( 2×π^2×ρ×v×f^2)
Now, put the values,
Sm = √( 10^-12 × 10^(84/10) ) / √( 2×(3.14)^2×1.21×346×(262)^2 )
Sm = √(2.51×10^-4 / 5.66×10^8)
Sm = √0.443×10^-12
Sm = 6.65×10^-13 m.
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.
Given: Mass m = 60 Kg
Weight W = 96 N
Required: Acceleration due to gravity, g = ?
Formula: W = mg
g = W/g
g = 96 Kg.m/s²/60 Kg (note: this is the derive unit for Newton "N")
g = 1.6 m/s²