Question 198: Gravitation

Question

A body A of mass m is moving in a circular orbit
of radius R about a planet. Another body B of
mass
$${m \over 2}$$
collides with A with a velocity which is half $$\left( {{{\overrightarrow v } \over 2}} \right)$$ the instantaneous velocity$${\overrightarrow v }$$
of A.
The collision is completely inelastic. Then, the
combined body :

Accepted Answer

Orbital speed for of A is v = $$\sqrt {{{GM} \over R}} $$
After collision, let the combined mass moves
with speed v
1
$$ 	herefore $$ mv + $${m \over 2}{v \over 2}$$ = $$\left( {{{3m} \over 2}} ight){v_1}$$
$$ \Rightarrow $$ v
1
= $${{5v} \over 6}$$
Since after collision, the speed is not equal to
orbital speed at that point. So motion cannot be
circular. Since velocity will remain tangential,
so it cannot fall vertically towards the planet.
Their speed after collision is less than escape
speed $$\sqrt 2 v$$, so they cannot escape
gravitational field.
So their motion will be elliptical around the
planet.

Answer

starts moving in an elliptical orbit around
the planet.

Answer

Falls vertically downwards towards the
planet

Answer

Escapes from the Planet's Gravitational field.

Answer

continues to move in a circular orbit

Gravitation

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