Question

two objects have the masses of 15kg and 10kg respectively. the 15kg object is placed on the surface of earth to 4m height and the 10kg one is placed to 2m height on a planet whose acceleration due to gravity is 2.5 times to that of earth surface. what is the ratio of their gravitational potential energies​

(take:gravitation of earth= 9.8m/s²)

Answer 1

Explanation:

According to universal law of gravitation the force attraction between two bodies is:-

F=(Gm1Gm2)/r2

when m1m2=The masses of two bodies,

r=Distance between them

G=Gravitational Force

when the distance is reduced to the half

r=(1/2)r then

F=(Gm1m2)/r2

=(Gm1Gm2)/(r/2)2

=(4 G m1m2)/ (r2)=4F

Therefore when the distance between the objects is reduced to half,then the force of gravitation increased by 4times the original orce

Answer 2

Answer:

The ratio of their gravitational potential energies​ is 6: 5.

Explanation:

Given,

The mass of object 1 is m₁ = 15 Kg

The mass of object 2 is m₂ = 10 Kg

The height of object placed on Earth (h₁) = 4 m

The height of object placed on unknown planet (h₂) = 2 m

And also the acceleration due to gravity on the unknown planet is 2.5 times to that of Earth.

i.e. gₓ = 2.5g

To find,

The ratio of gravitational potential energies of both objects.

Calculation,

The gravitational potential energy (P) = mgh

For object 1:

gravitational potential energy (P₁) = m₁gh₁

⇒ P₁ = 15 Kg × g × 4 m

⇒ P₁ = 60g

For object 2:

gravitational potential energy (P₂) = m₂gₓh₂

⇒ P₂ = 10 Kg × 2.5g × 2 m

⇒ P₂ = 50g

Hence,

P₁/P₂ = 60g/50g

⇒ P₁/P₂ = 6/5

Therefore, the ratio of their gravitational potential energies​ is 6: 5.

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