Question

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​

Answer 1

Answer:

The formula for gravitational force is :

F = G×m1×m2 / r2

G (gravitational constant) = 6.67×10-11m3 kg-1 s-2

m1(mass of the object) = 100 kg

m2(mass of the earth) = 5.972 × 1024 kg

r (radius of the earth) = 6371 km

Now putting the values in the given:

F = 6.67 × 10-11 × 100 × 5.972 × 1024/ (6371)2  

On calculation it equals to:

F=39.83324 ×  1015 / 40589641  

F=9.81 × 108 N

To find the acceleration use the formula

F = Ma

So force for both cases is F=9.81 × 108 N

Acceleration on the body is:

F = Ma

So force on body is F=9.81 × 108 N and M=100kg

a= 9.81 × 108 / 100= 9.81 x 106 m/s2

Now force on earth is F=9.81 × 108 N and m2(mass of the earth) = 5.972 × 1024 kg

a= 9.81 × 108 N  / 5.972 × 1024 kg

Acceleration on earth is 1.64 × 10-16 kg

Regards

Answer 2

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According to universal law of gravitation the force of attraction between two bodies is directly proportional to product of their masses and inversely proportional to square of distance between them . This law can be represented by the equation :-

$\maltese \: f = \frac{GMm}{ {d}^{2} }$

Here G is universal gravitational constant = 6.673 × 10^-11

Now we have been given that :

• Mass of body = 100kg
• Mass of earth = 5.97 × 10^24kg.
• Radius of earth = 6371km
• Force of attraction between bodies = ?

Now after inputting these values in universal law of gravitation we get :-

$\maltese \: f \: = \frac{6.673 \times {10}^{ - 11} \times 5.972 \times {10}^{24} \times 100}{ {6371}^{2} }$

After solving a bit we get :-

$f = 9.8 \times {10}^{8} n$

Therefore we get that force of attraction between body and earth is 9.8 × 10^8N.

Now, acceleration produced in body will be :

We know F =ma

$\therefore \: a = \frac{f}{m}$

After inputting the values we get :-

$a = \frac{9.8 \times {10}^{8} }{100}$

$a = 9.8 \times {10}^{6}$

Therefore acceleration of the body is 9.8 × 10^6.

Now acceleration produced in earth will be :-

$a = \frac{9.8 \times {10}^{8} }{5.972 \times {10}^{24} }$

$a = 1.6 \times {10}^{ - 16}$

Therefore acceleration produced in earth will be 1.6 × 10^-16.

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BY SCIVIBHANSHU

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