Question

A man can jump to a height of 1.5 m on a planet A what is the height ne may be able to jump on another planet whose density and radius are respectively one-quarter and one-third that of planet A

(A) 1.5 m

(B) 15 m

(C) 18 m

(D) 28 m

Answer 1

Correct option: (C) 18 m

Explanation:

Given = h1 = 1.5m

ρ2 = (1/4)ρ1

R2 = (1/3)R1

∵ g = (GM / R2)

= (G/R2) × (4/3)πR3 × ρ

g = (4/3)πRρG

i.e. g ∝ Rρ

(g2 / g1) = (R2 / R1) ∙ (ρ2 / ρ1)

(g2 / g1) = (1/3) × (1/4) = (1 / 12)

12g2 = g1

Now V2 = U02 + 2gs

i.e. V2 = 2gh -------- initial velocity = 0

h = (V2 / 2g)

h ∝ (1/g)

(h2 / h1) = (g1 / g2)

hence h2 = h1 × (g1 / g2) = 12h1

h2 = 12 × h1 = 12 × 1.5 = 18 m