Answer:
Option (c) u0
Explanation:
The escape velocity has a formula as:
V = √(2gR)
Where V is the escape velocity,
g is the acceleration due to gravity
R is the radius of the earth.
Now, from the question, we were told that the escape velocity for the rocket taking off from earth is u0 i.e
V(earth) = u0
V(earth) = √(2gR)
u0 = √(2gR) => For the earth
Now, let us calculate the escape velocity for the rocket taking off from planet x. This is illustrated below below:
g(planet x) = 2g (earth) => since the weight of the astronaut is twice as much on planet x as on earth
R(planet x) = 1/2 R(earth) => planet x has half the radius of earth
V(planet x) =?
Applying the formula V = √(2gR), the escape velocity on planet x is obtained as follow:
V(planet x) = √(2g(x) x R(x))
V(planet x) = √(2 x 2g x 1/2R)
V(planet x) = √(2 x g x R)
V(planet x) = √(2gR)
The expression obtained for the escape velocity on planet x i.e V(planet x) = √(2gR), is exactly the same as that obtained for the earth i.e V(earth) = √(2gR)
Therefore,
V(planet x) = V(earth) = √(2gR)
But from the question, V(earth) is u0
Therefore,
V(planet x) = V(earth) = √(2gR) = u0
So, the escape velocity on planet x is u0
