JEE Main · 2012 · 29 Apr 2012 · Offline · Gravitation

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 / s^{2}

and 6400km respectively. The required energy for this work will be ;

(A) $6.4 \times 1 0^{11}$ Joules
(B) $6.4 \times 1 0^{8}$ Joules
(C) $6.4 \times 1 0^{9}$ Joules
(D) $6.4 \times 1 0^{10}$ Joules✓ Correct

Answer: (D)

Solution

To send the ship from the surface out to where gravity no longer binds it, the launch must supply energy equal in magnitude to the gravitational potential energy it holds at the surface, namely

\frac{GM m}{R}

. Using

g = \frac{GM}{R ^{2}}

this is simply

m g R

. Substituting

m = 1000

kg,

g = 10 m/ s^{2}

and

R = 6400 km = 6.4 \times 1 0^{6}

m gives

E = 1000 \times 10 \times 6.4 \times 1 0^{6} = 6.4 \times 1 0^{10}

joules.

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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JEE Main · 2012 · 29 Apr 2012 · Offline · Gravitation

Solution

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