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Q.

A spherical planet of radius R has a uniform density $ρ$ and does not rotate. If the planet is made up of some liquid, the pressure at any point at distance r from the centre is $η π G ρ^{2} (R^{2} - r^{2}) .$ Find $η$ ?

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answer is 0.67.

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Detailed Solution

$\int_{0}^{P} d P = - \int_{R}^{r} \frac{4 π G ρ^{2}}{3} r d r = \frac{2 π G ρ^{2}}{3} (R^{2} - r^{2}) [η = 0.67]$

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A spherical planet of radius R has a uniform density ρ and does not rotate. If the planet is made up of some liquid, the pressure at any point at distance r from the centre is ηπGρ2(R2−r2). Find η ?