Question

find the gravitational force acting between earth and 1kg object when Me =6*1024andRe =6.4*106​

Answer 1

$\underline{ \boxed{ \bold{ \mathfrak{ \huge{ \purple{Answer}}}}}}$

Given :

mass of object = 1 kg

mass of earth = $\rm\:6×{10}^{24} \: kg$

distance = $\rm\:6.4×{10}^{6}\:m$

To Find :

Gravitational force between earth and object...

Formula :

Formula of gravitational force between two mass is given by...

$\dag \: \: \underline{ \boxed{ \bold{ \pink{ \rm{f = \frac{GMm}{ {r}^{2} } }}}}} \: \red{ \star}$

Calculation :

$\implies \rm \: F = \frac{6.67 \times {10}^{ - 11} \times \: 6 \times {10}^{24} \times 1}{ {(6.4 \times {10}^{6} )}^{2} } \\ \\ \therefore \: \boxed{ \rm{ \orange{F = 9.8 \: N}}} \: \red{ \star}$

Answer 2

$\huge \fcolorbox{red}{pink}{Solution :)}$

The Newton's law of universal gravitation states that the force between two object in the universe is directly proportional to the product of their masses and inversely proportional to the square of distance between them

Given ,

Mass of object (m1) = 1 kg

Mass of earth (m2) = 6 × (10)^24

Distance between them (r) = 6.4 × (10)^6

We know that , the Newton's law of universal gravitation is given by

$\large \mathtt{ \fbox{F = \frac{ G \times m_{1}m_{2} }{ {(r)}^{2} } }}$

Where , G = universal gravitational constant , which is 6.67 × (10)^-11 Nm²/Kg²

Substitute the known values , we get

$\sf \hookrightarrow F = \frac{6.67 \times {(10)}^{ - 11} \times 1 \times 6 \times {(10)}^{24} }{ {(6.4)}^{2} \times {(10)}^{12} } \\ \\ \sf \hookrightarrow F = \frac{667 \times {(10)}^{ - 11} \times 6 \times {(10)}^{24} \times {(10)}^{2} }{ {(10)}^{2} \times 4096 \times {(10)}^{12} } \\ \\ \sf \hookrightarrow F = \frac{667 \times6 \times {(10)}^{ - 11 + 24 + 2 - 2 - 12} }{4096} \\ \\ \sf \hookrightarrow F = 0.977 \times {(10)}^{1} \\ \\ \sf \hookrightarrow F = 9.77 \: \: newton$

Hence , the gravitational force acting between earth and object is 9.77 newton

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