First slide

Gravitational field intensity

Question

Weight of a body on the surfaces of two planets is the same. If their densities are d₁ and d₂, then the ratio of their radius

Easy

A

$\large \frac {d_1}{d_2}$
B

$\large \frac {d_2}{d_1}$
C

$\large \frac {d_1^2}{d_2^2}$
D

$\large \frac {d_2^2}{d_1^2}$

Solution

$\large g=\frac43\pi dG$
W = mg If weight W remains constant, g also remains constant.
$\large \therefore d\propto 1/R$
$\large \therefore \frac {R_1}{R_2}=\frac {d_2}{R_1}$

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