The escape velocity for the earth is 11.2 km/s. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet isa)280 km/sb)56.0 km/sc)112 km/sd)56 km/sCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Escape velocity of Earth = 11.2 km/s
Mass of another planet = 100 times mass of earth
Radius of another planet = 4 times radius of earth

To find: Escape velocity of the planet

Formula used: Escape velocity (v) = √(2GM/R), where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

Calculation:
Let the mass of the planet be M and its radius be R.
Given, M = 100M_{Earth}, R = 4R_{Earth}
Escape velocity of the planet, v = √(2GM/R)

We know that escape velocity is directly proportional to the square root of mass and inversely proportional to the square root of radius. Therefore, we can write:

v/v_{Earth} = √(M/M_{Earth})/√(R/R_{Earth})
v/11.2 = √(100)/√4
v/11.2 = 10/2
v = 56 km/s

Therefore, the escape velocity of the planet is 56 km/s, which is option (B).

Answer

Answer

On earth velocity of (escape)=(2GM÷R)^0.5 On ' other planet' V' = 5 velocity of escape on earth =5×11.2= 56.0km/s

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