Question

A rocket lifts a payload upward from the surface of Earth. The radius of Earth is R, and the weight of the payload on the surface of Earth is W. The force of Earth's gravity on the payload is W/2 when the rocket's distance from the center of the Earth is
A. R
B. sqrt(2)R
C. 2R
D. 2sqrt(2)R
E. 4R

Answer 1

Answer:

the correct answer is B      r =√2   R

Explanation:

To solve this exercise we will use the force of gravity, at two points when the rocket is on the platform and when it is at the desired height.

Rocket with cargo on the platform

              $F_{g} = G \frac{ m M }{R^2} = W$

where m is the mass of the rocket and the charge, M the mass of the earth and R the distance from the center of the earth

Rocket loaded at desired height

              $F_{g} = G \frac{m M}{r^2 } = \frac{W}{2}$

we write our two equations

        W = g m M / R²

        $\frac{W}{2}$ = G m M / r²

we match to solve them

         Gm M / R² = 2 Gm M / r²

         1 / R² = 2 / r²

          r =√2   R

therefore the correct answer is B