Question

The ratio of radii of earth to another planet is 2/3 and the ratio of their mean densities is 4/5. If an astronaut can jump to a maximum height of 1.5 m on the earth, with the same effort, the maximum height he can jump on the planet is

Answer 1

Hey dear,

◆ Answer-
h' = 0.8 m

◆ Explaination-
# Given-
R/R' = 2/3
ρ /ρ' = 4/5
h = 1.5 m

# Solution-
Mass of the earth is calculated by-
M = ρV
M = ρ × 4/3 πR^3

Gravitational acceleration at earth's surface is -
g = GM/R^2
g = G × ρ × 4/3 πR^3 / R^2
g = 4/3 πRρG

Similarly, gravitational acceleration at given planet's surface is-
g' = 4/3 πR'ρ'G

Let E be common energy provided to man of mass m on both planets.
At max. height this energy is converted to potential energy.
mgh = mg'h'
h' = gh / g'
h' = (4/3 πRρG)h / 4/3 πR'ρ'G
h' = Rρh / R'ρ'
h' = 2/3 × 4/5 × 1.5
h' = 0.8 m

Therefore, the man can jump to max height of 0.8 m.

Hope it helps...