CSIR-NET 2015
22. In order to have the same value of the surface acceleration due to gravity as on earth, a planet twice its radius must have a mean relative density of.
1)2.75
2)5.5
3)1.4 4)2.25
Solution:
Formula,
Acceleration due to
gravity, g=\frac{Gm}{r^2}---(1)
From the above problem,
we need a relation between the radius and density.
So,
Density=
\frac{mass}{volume}
mass=Density\times
volume
m=\rho \times v ---(2)
Substitute equation (2)
in equation (1)
g= \frac{G\times
\rho\times v}{r^2}
then,
\frac{G\times
\rho_1\times v_1}{r_1^2}= \frac{G\times \rho_2\times v_2}{r_2^2}---(3)
Volume of the Earth and
planets are, v=\frac{4}{3}\pi r^3
Substitute the above volume
information in equation (3)
\frac{G\times
\rho_1\times \frac{4}{3}\pi r_1^3}{r_1^2}= \frac{G\times \rho_2\times
\frac{4}{3}\pi r_2^3}{r_2^2}
Therefore simplifying the
above equation we get,
\rho_1\times
r_1=\rho_2\times r_2
\frac{\rho_2}{\rho_1}=\frac{r_1}{r_2}---(4)
From above problem
r_2=2\times r_1
\rho_1=5.5 gm/cc Earth
density
Substitute above values
in equation (4)
\frac{\rho_2}{\rho_1}=\frac{r_1}{2
\times r_1}
\frac{\rho_2}{\rho_1}=\frac{1}{2}
\rho_2=\frac{5.5}{2}
\rho_2=2.75 gm/cc
Get SEE science notes from here: Acceleration due to gravity g | Solved | SEE Grade 10 | Science
ReplyDeleteThanks! It was cool. I was attempting advanced eq with no result.😅
ReplyDeleteYou are welcome.
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