Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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 :

VirαtKσhli

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]

View image VirαtKσhli
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.