Question

ix) Aplanet has mass 6.4x10^24kg and radius
3.4x10^6 m. Calculate energy required to
remove on object of mass 800 kg from
the surface of the planet to infinity.
[Ans: 1.004 X10^10)J]​

Answer 1

answer : 10.04 × 10^10 J

mass of a planet, M = 6.4 × 10²⁴ kg

radius of the planet , r = 3.4 × 10^6 m

we have to find energy required to remove an object of mass m = 800 kg from the surface of the planet to infinity.

using formula, U = GMm/r

= 6.67 × 10-¹¹ × 6.4 × 10²⁴ × 800/(3.4 × 10^6)

= 10.04 × 10^10 J

hence 10.04 × 10^10 J energy required to remove an object of mass 800 kg from the surface of planet to infinity.

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

126.1 MJ/kg

Explanation:

Mass of planet = 6.4×10^24 kg

Radius = 3.4×10^6 m

G = 6.7*10^(-11) Nm^2/kg^2

The gravitational potential at surface is:

P = -(G*M)/r

= - [6.7*10^(-11) × 6.4×10^24 ]/3.4×10^6

= - 12.61 × 10^7

= -1.261 × 10^8 J/kg

P= -126.1 MJ/kg

Now if 10MJ/kg work is done to lift a particle to some height from surface the potential will be -116.1 MJ/kg .

So, the required work = 126.1 MJ/kg

[raised to a height where gravitational potential reaches zero . From 0 to infinity it can not be measured ]