First slide

Gravitational field intensity

Question

Mass of the earth is 81 times that of the moon. If the distance between their centers is d, then the point on the line joining their centers at which the gravitational field due to them is zero is

Easy

A

d/10 from the center of moon
B

d/10 from the center of earth
C

9d/10 from the center of moon
D

d/2 from each other

Solution

$\large \vec I_P=\vec I_1+\vec I_2=0$
$\large \Rightarrow \frac {Gm_1}{x^2}-\frac {Gm_2}{(d-x)^2}=0$
$\large \Rightarrow x=\frac {d}{\left ( \sqrt \frac {m_2}{m_1}+1 \right )}=\frac {d}{\left ( \sqrt \frac {81M}{M}+1 \right )}$
$\large \Rightarrow x=d/10$

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