Question

A car weighs 6000 N on the Earth's surface, what is its weight 3 times

Earth's radius away from the center of the Earth? (N)

Answer 1

667 N

Step-by-step explanation:

`\pink{\frak{Given}}\Bigg\{ \textsf{ A car weighs 6000 N on the Earth's surface.}`

And we need to find out the weight of the car at a distance equal to 3 times the radius of the earth , from the centre of the earth.

We can find the acceleration due to gravity at a height h from the earth's surface as ,

`\sf\longrightarrow \red{ g_h = g\bigg[ 1 +(h)/(R_e)\bigg]^(-2)}`

• The height here will be 3R - R = 2R , since 3R is the distance from the centre of the earth .

In above equation multiply both sides by m ,

`\sf\longrightarrow mg_h = mg\bigg[ 1 +(h)/(R_e)\bigg]^(-2)`

Now here at the place of mg we can substitute 6000N , and mg
`_h` will be the weight at height h which we are interested in finding .

`\sf\longrightarrow W_h = 6000 \bigg[ 1 +(2R)/(R)\bigg]^(-2)\\`

`\sf\longrightarrow W_h = 6000 [ 1 + 2 ]^(-2)\\`

`\sf\longrightarrow W_h = 6000 [ 3]^(-2)\\`

`\sf\longrightarrow W_h = 6000 * (1)/(3^2)=(6000)/(9)\\`

`\sf\longrightarrow \boxed{\bf Weight_h = 667N \ \ (approx) }`