Question

What is the gravitational force between two identical 5000 kg asteroids whose centers are apart by 100 m?

Answer 1

`F=1.6675*10^-7N`

Explanation:

For this,you must know how to behave with Scientific Notations

Use the Newton's law of Gravitation formula

`color(brown)(F=G(m_1m_2)/(r^2)`

Here are the definition of the variables in the formula

`color(blue)("F"="Force of Gravity"`

`color(blue)("G"="Gravitational constant"=6.67*10^-11 N(m^2)/(kg^2)`

`color(blue)(m_1="Mass of the first object"="5000 kg"`

`color(blue)(m_2="Mass of second object=""5000 kg"`

`color(blue)(r="Distance between the centres of the objects"="100 m"`

We need to find `F`

Before entering the values, we must convert the mass and the distance values into scientific notation (in the form of exponents)

`color(violet)(m_1="5000 kg"=5*1000=5*10^3` `color(violet)("kg"`

`color(violet)(m_2="5000 kg"=5*1000=5*10^3` `color(violet)("kg"`

`color(violet)(r="100 m"=10^2` `color(violet)("m"`

Now, substitute the values in the formula

`rarrF=6.67*10^-11 N(m^2)/(kg^2)((5*10^3kg)(5*10^3kg))/((10^2m)^2)`

We have `(5*10^3kg)(5*10^3kg)=(5*10^3kg)^2`

`rarrF=6.67*10^-11 N(m^2)/(kg^2)((5*10^3kg)^2)/(10^4m^2)`

`rarrF=6.67*10^-11 N(m^2)/(kg^2)(5^2*10^6kg^2)/(10^4m^2)`

`rarrF=6.67*10^-11 N(m^2)/(kg^2)(25*10^6kg^2)/(10^4m^2)`

Now we start to cancel

`rarrF=6.67*10^-11 N(cancel(m^2))/(cancel(kg^2))(25*10^6cancel(kg^2))/(10^4cancel(m^2))`

`rarrF=6.67*10^-11N(25*10^6)/10^4`

`rarrF=(6.67*10^-11*25*10^6)/10^4N`

`rarrF=(166.75*10^-5)/10^4N`

Move `10^4` to the Numerator

Remember that,when positive exponents in the Denominator go to the Numerator,the become as Negative exponents

`rarrF=166.75*10^-5*10-4N`

`rarrF=166.75*10^-9`

`color(green)(rArrF=1.6675*10^-7`

If you need more guidance for the Newton's Gravitation formula

Watch