Question

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

Answer 1

Answer:

667 N

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 ,

$\sf\longrightarrow \red{ g_h = g\bigg[ 1 +\dfrac{h}{R_e}\bigg]^{-2}}$

• 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 ,

$\sf\longrightarrow mg_h = mg\bigg[ 1 +\dfrac{h}{R_e}\bigg]^{-2}$

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 .

$\sf\longrightarrow W_h = 6000 \bigg[ 1 +\dfrac{2R}{R}\bigg]^{-2}$

$\sf\longrightarrow W_h = 6000 [ 1 + 2 ]^{-2}$

$\sf\longrightarrow W_h = 6000 [ 3]^{-2}$

$\sf\longrightarrow W_h = 6000 \times \dfrac{1}{3^2}=\dfrac{6000}{9}$

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