Question

a boy can jump h m high on the earth. the height (in metre) he might be able to jump on a plant whose density is one eighth of the density of earth and radius is twice the radius of earth, is -
(a) 2h (b) 4h (c) 8h (d)16h (e) none of these

Answer 1

hey there is answer !!
I hope you help !!
_see the picc

Answer 2

Relation between acceleration due to gravity (g) & gravitational force (G) is

g = ( G.M ) / R² [ M = mass of planet ; R = radius of planet ]

Lets assume, g₁ , M₁ , R₁ , V₁ , D₁ are assigned to earth [D is density of the planet]

where g₂ , M₂ , R₂ , V₂ , D₂ is for the other planet [ V is volume of the planet]

V = (4/3) . π . R³ ⇒ V ∞ R³

As per question,

D₂ = D₁ / 8

& R₂ = 2.R₁

Thus (V₁/V₂) = (R₁³/R₂³) = (R₁³ / 8.R₁³)

⇒ V₂ = 8.V₁ .......A

Now, D₁ = M₁ / V₁ & D₂ = M₂ / V₂

or, M₁ / V₁ = 8.M₂ / V₂

or, M₁ / V₁ = 8.M₂ / (8.V₁) [ value of V₂ from equation A ]

or, M₁ = M₂

Therefore, (g₁ / g₂) = (R₂² / R₁²)

or,  (g₁ / g₂) = (4.R₂² / R₂²)

or, g₂ / 4 = g₁ ..........B

While jumping the initial velocity of the boy was same in both planets,

following this formula; u² = 2.g.h

⇒ 2.g₁.h₁ = 2.g₂.h₂

or, 4.g₂.h = g₂.h₂ [ value of g₁ from equation B ]

or, 4.h = h₂

Thus on that planet the boy will jump 4h m (option b)