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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)

Sagot :

VirαtKσhliidn

Answer:

667 N

Explanation:

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

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 ,

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

  • 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 ,

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

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

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

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

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

[tex]\sf\longrightarrow W_h = 6000 \times \dfrac{1}{3^2}=\dfrac{6000}{9}\\ [/tex]

[tex]\sf\longrightarrow \boxed{\bf Weight_h = 667N \ \ (approx) } [/tex]

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