A research satellite of mass 200 ,kg circles | vedclass

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(A) The gravitational force on a mass $m$ at a distance $r$ from the center of the earth is given by $F = G \frac{Mm}{r^2}$.Given the gravitational pu

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$889$

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(A) The gravitational force on a mass $m$ at a distance $r$ from the center of the earth is given by $F = G \frac{Mm}{r^2}$.Given the gravitational pull on $1 \,kg$ at the surface $(r = R)$ is $10 \,N$,we have $g = 10 \,m/s^2$.The gravitational acceleration $g'$ at an orbital radius $r = 3R/2$ is given by $g' = g \left( \frac{R}{r} ight)^2$.Substituting $r = 3R/2$,we get $g' = g \left( \frac{R}{3R/2} ight)^2 = g \left( \frac{2}{3} ight)^2 = \frac{4}{9}g$.The gravitational pull on the satellite of mass $m = 200 \,kg$ is $F' = m 	imes g' = 200 	imes \frac{4}{9} 	imes 10$.$F' = \frac{8000}{9} \approx 888.89 \,N$.Rounding to the nearest integer,we get $889 \,N$.

$A$ research satellite of mass $200 \,kg$ circles the earth in an orbit of average radius $3R/2$,where $R$ is the radius of the earth. Assuming the gravitational pull on a mass of $1 \,kg$ on the earth's surface to be $10 \,N$,the pull on the satellite will be ........ $N$.

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