For multiple choice questions, circle the one best answer or letter (unless more

Question

For multiple choice questions, circle the one best answer or letter (unless more than one answer is asked for). Show your work on free-response questions. Be sure to use proper units and significant figures in our final answers. Organization and neatness count, too. Do NOT use red ink - please reserve that color for grading. Suppose that a more massive planet M_1 and a less massive planet M_2 are located distance d apart, as shown above. Let M_1 = 6M_2 (namely, M_1 is 6 times as massive as M_2). Find the location of the point in space between the two planets where a small object m would experience a net gravitational force of zero. Express your answer EITHER as fully simplified exact arithmetic expression using d, OR as a decimal fraction of d expressed to 3 significant figures. State whether the distance in hour answer is measured to the right of M_1 or measured to the left of M_2. Mark and label this point on the diagram above.

Explanation / Answer

Force exerted by M1 = Force exerted by M2

let x be the distance from M1 towards M2 where m experiences zero force

then

G*M1*m/(x^2) = G*M2*m/(d-x)^2

since M1 = 6M2

then

G*6*M2*m/x^2 = G*M2*m/(d-x)^2

6/x^2 = 1/(d-x)^2

(d-x)/x = sqrt(1/6) = 0.408

d-x = 0.408*x

x = d/1.408

to the right of M1

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