Assuming density d of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to

Question

Assuming density d of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to (A)  d  (B)  √d  (C)  1/√d  (D)  1/d

Tardigrade Admin · Accepted Answer

Density of the Planet can be written as ρ=(m/v)=(m/(4)3 π a3) ⇒ ρ propto (1/a3) According to Kepler's law, T2 propto a3 ⇒ T2 propto (1/ρ) or T propto (1/√ρ)=(1/√d) [∵ ρ=d]

Q. Assuming density $d$ of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to

$d$

$d$

$1/ d$

$1/ d$

Density of the Planet can be written as
$ρ = \frac{m}{v} = \frac{m}{\frac{4}{3} π a ^{3}}$
$\Rightarrow ρ \propto \frac{1}{a ^{3}}$
According to Kepler's law, $T^{2} \propto a^{3}$
$\Rightarrow T^{2} \propto \frac{1}{ρ}$
or $T \propto \frac{1}{ρ} = \frac{1}{d}$
$[∵ ρ = d]$

Q. Assuming density d of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to

d

d​

1/d​

1/d

Density of the Planet can be written as ρ=vm​=34​πa3m​ ⇒ρ∝a31​ According to Kepler's law, T2∝a3 ⇒T2∝ρ1​ or T∝ρ​1​=d​1​ [∵ρ=d]

Q. Assuming density $d$ of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to

$d$

$d$

$1/ d$

$1/ d$

Density of the Planet can be written as
$ρ = \frac{m}{v} = \frac{m}{\frac{4}{3} π a ^{3}}$
$\Rightarrow ρ \propto \frac{1}{a ^{3}}$
According to Kepler's law, $T^{2} \propto a^{3}$
$\Rightarrow T^{2} \propto \frac{1}{ρ}$
or $T \propto \frac{1}{ρ} = \frac{1}{d}$
$[∵ ρ = d]$