A body weights 450 N on the surface of Earth . How much will it weigh on the surface of a planet whose masss is 1/9th mass of Earth and rad

Question

A body weights 450 N on the surface of Earth . How much will it weigh on the surface of a planet whose masss is 1/9th mass of Earth and radius is half of radius of Earth?​

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Kim Cúc 3 years 2021-08-06T16:48:31+00:00 1 Answers 22 views 0

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  1. mocmien2
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    2021-08-06T16:50:29+00:00
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    Answer:

    The weight of the body on the other planet would be 200 N

    Explanation:

    Recall that the acceleration of gravity at sea level on Earth is obtained via the general Gravitational force formula when the distance “d” is the radius of the Earth (R):

    F=m\,g=G\,\frac{m\,\,m_E}{R^2} = m \,(G\,\frac{m_E}{R^2} )

    We are told that the weight of the object on Earth is 450 N, that is:

    W=m\,g= m \,(G\,\frac{m_E}{R^2} )= 450

    in this other planet the acceleration of gravity will be different as shown below:

    (G\,\frac{m_E\,(1/9)}{(R/2))^2} )=(G\,\frac{m_E\,\,4}{R^2\,\,9} )=\frac{4}{9} (G\,\frac{m_E}{R^2} )

    so, its gravity is 4/9 that of the Earth, which now we can use to convert its weight (w) on the planet as 4/9 the weight it has on Earth:

    w=m\,g_p=m\,\frac{4}{9} \,g=\frac{4}{9} \,450= 200\,\, N

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