Question 181: Gravitation

Question

Planet A has mass M and radius R. Planet B has
half the mass and half the radius of Planet A.
If the escape velocities from the Planets A and
B are v
A
and v
B
, respectively, then $${{{v_A}} \over {{v_B}}} = {n \over 4}$$.
The value of n is :

Accepted Answer

Escape velocity, V
e
= $$\sqrt {{{2GM} \over R}} $$
V
A
= $$\sqrt {{{2GM} \over R}} $$
V
B
= $$\sqrt {{{2G{M \over 2}} \over {{R \over 2}}}} $$ = $$\sqrt {{{2GM} \over R}} $$
$${{{V_A}} \over {{V_B}}}$$ = 1
Given $${{{V_A}} \over {{V_B}}} = {n \over 4}$$
$$ 	herefore $$ $${n \over 4}$$ = 1
$$ \Rightarrow $$ n = 4

Answer

1

Answer

2

Answer

4

Answer

3

Gravitation

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are v A and v B , respectively, then ${{{v_A}} \over {{v_B}}} = {n \over 4}$. The value of n is :

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