# Calculate the gravitational force between a body of mass 100 kg and the earth. Also?calculate the acceleration produced in the body and that in earth. ?

ββββThe formula for gravitational force is :

F = G×m

_{1}×m

_{2}/ r

^{2}

G (gravitational constant) = 6.67×10

^{-11}m

^{3}kg

^{-}

^{1}s

^{-}

^{2}

m

_{1}(mass of the object) = 100 kg

m

_{2}(mass of the earth) = 5.972 × 10

^{24}kg

r (radius of the earth) = 6371 km

Now putting the values in the given:

F = 6.67 × 10

^{-11}× 100 × 5.972 × 10

^{24}/ (6371)

^{2 }

On calculation it equals to:

F=39.83324 × 10

^{15}/ 40589641

^{ }

F=9.81 × 10

^{8}N

To find the acceleration use the formula

F = Ma

So force for both cases is F=9.81 × 10

^{8}N

Acceleration on the body is:

F = Ma

So force on body is F=9.81 × 10

^{8}N and M=100kg

a= 9.81 × 10

^{8}/ 100= 9.81 x 10

^{6}m/s

^{2}

Now force on earth is F=9.81 × 10

^{8}N and m

_{2}(mass of the earth) = 5.972 × 10

^{24}kg

a= 9.81 × 10

^{8}N / 5.972 × 10

^{24}kg

Acceleration on earth is 1.64 × 10

^{-16}kg

Regards

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