JEE MAIN - Physics (2020 - 9th January Evening Slot - No. 9)
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 vA and vB, respectively, then $${{{v_A}} \over {{v_B}}} = {n \over 4}$$.
The value of n is :
1
2
4
3
Explanation
Escape velocity, Ve = $$\sqrt {{{2GM} \over R}} $$
VA = $$\sqrt {{{2GM} \over R}} $$
VB = $$\sqrt {{{2G{M \over 2}} \over {{R \over 2}}}} $$ = $$\sqrt {{{2GM} \over R}} $$
$${{{V_A}} \over {{V_B}}}$$ = 1
Given $${{{V_A}} \over {{V_B}}} = {n \over 4}$$
$$ \therefore $$ $${n \over 4}$$ = 1
$$ \Rightarrow $$ n = 4
VA = $$\sqrt {{{2GM} \over R}} $$
VB = $$\sqrt {{{2G{M \over 2}} \over {{R \over 2}}}} $$ = $$\sqrt {{{2GM} \over R}} $$
$${{{V_A}} \over {{V_B}}}$$ = 1
Given $${{{V_A}} \over {{V_B}}} = {n \over 4}$$
$$ \therefore $$ $${n \over 4}$$ = 1
$$ \Rightarrow $$ n = 4
Comments (0)
