JEE Main 2026 — Jan 22, Shift 1 — Physics solution

JEE Main2026Jan 22, Shift 1Physics

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is _______ m/s.

A
1000
B
$2005$
C
$10010$
D
$10002$

Solution

$v_{e} = \frac{2 GM}{R}$ . With $M = ρ \cdot \frac{4 π R ^{3}}{3}$ , this becomes $v_{e} = \frac{8 π Gρ R ^{2}}{3} \propto ρ R$ .

So $\frac{( v _{e} ) _{B}}{( v _{e} ) _{A}} = \frac{ρ _{B}}{ρ _{A}} \cdot \frac{R _{B}}{R _{A}} = 0.1 \times 0.1 = \frac{1}{10 10}$ .

Therefore $(v_{e})_{B} = \frac{10000}{10 10} = \frac{1000}{10} = 10010$ m/s.

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