How much energy will be necessary for making a body of 500 kg escape from the earth? [ g =9.8 ms 2., radius of the earth .6.4 × 106 m ]

Question

How much energy will be necessary for making a body of 500 kg escape from the earth? [ g =9.8 ms 2., radius of the earth .6.4 × 106 m ] (A) About 9.8× 106J  (B) About 6.4× 108J  (C) About 3.1× 1010J  (D) About 27.4× 1012J

Tardigrade Admin · Accepted Answer

Escape velocity ve=√2 g R Kinetic energy of the body required to escape K E=(1/2) m ve2 or K E=(1/2) m(2 g R) or K E=m g R or K E=500 × 9.8 × 6.4 × 106 ⇒ K E=3.1 × 1010 J

Q. How much energy will be necessary for making a body of $500 k g$ escape from the earth? $[g = 9.8 m s^{2}$ , radius of the earth $6.4 \times 1 0^{6} m]$

About $9.8 \times 1 0^{6} J$

About $6.4 \times 1 0^{8} J$

About $3.1 \times 1 0^{10} J$

About $27.4 \times 1 0^{12} J$

Escape velocity $v_{e} = 2 g R$
Kinetic energy of the body required to escape
$K E = \frac{1}{2} m v_{e}^{2}$
or $K E = \frac{1}{2} m (2 g R)$
or $K E = m g R$
or $K E = 500 \times 9.8 \times 6.4 \times 1 0^{6}$
$\Rightarrow K E = 3.1 \times 1 0^{10} J$

Q. How much energy will be necessary for making a body of 500kg escape from the earth? [g=9.8ms2, radius of the earth 6.4×106m]

About 9.8×106J

About 6.4×108J

About 3.1×1010J

About 27.4×1012J