The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be :

Question

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be : (A) 6.4 × 1011 Joules (B) 6.4 × 108 Joules (C) 6.4 × 109 Joules (D) 6.4 × 1010 Joules

Tardigrade Admin · Accepted Answer

W=0-(-(GMm/R))=(GMm/R) =gR2× (m/R)=mgR = 1000 Ã 10 Ã 6400 Ã 103 = 64 Ã 109 J = 64 Ã 1010

Q. The mass of a spaceship is $1000 k g$ . It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth) are $10 m / s^{2}$ and $6400 km$ respectively. The required energy for this work will be :

$6.4 \times 1 0^{11}$ Joules

$6.4 \times 1 0^{8}$ Joules

$6.4 \times 1 0^{9}$ Joules

$6.4 \times 1 0^{10}$ Joules

$W = 0 - (- \frac{GM m}{R}) = \frac{GM m}{R}$
$= g R^{2} \times \frac{m}{R} = m g R$
$= 1000 \times 10 \times 6400 \times 1 0^{3}$
$= 64 \times 1 0^{9} J$
$= 64 \times 1 0^{10}$

Q. The mass of a spaceship is 1000kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10m/s2 and 6400km respectively. The required energy for this work will be :

6.4×1011 Joules

6.4×108 Joules

6.4×109 Joules

6.4×1010 Joules