Question

the distance between the centres of the earth and the moon is 60 times the radius of the earth.calculate the centripetal acceleration of the moon. acceleration due to gravity on the earth's surface =10m/s2

Answer 1

Answer:

the centripetal acceleration of the moon =1/360 m/s^2

Explanation:

GMe/(60R)^2=centripetal acc.

g/3600=centripetal acc.

1/360= centripetal acc.

Answer 2

Given that,

The distance between the centres of the earth and the moon is 60 times the radius of the earth.

To find,

The centripetal acceleration of the moon. acceleration due to gravity on the earth's surface.

Solution,

For uniform circular motion, centripetal acceleration is given by :

$a=\dfrac{v^2}{r}$

From Newton’s Universal law of gravity, acceleration is given by :

$g=\dfrac{GM}{R_e^2}$

Since, the distance between the centres of the earth and the moon is 60 times the radius of the earth. So,

$a=\dfrac{GM}{(60R_e)^2}\\\\a=\dfrac{g}{3600}\\\\a=\dfrac{10}{3600}\\\\a=0.0027\ m/s^2\\\\a=3\ mm/s^2$

So, the centripetal acceleration of the moon is $3\ mm/s^2$.

Learn more,

Acceleration due to gravity

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