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

ID: 1548016 • Letter: F

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 your 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 - 7M_2 (namely, M_1 is 7 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 final answer EITHER as a fully simplified exact arithmetic expression using d, OR as a decimal fraction of d expressed to 3 significant figures. State whether the distance in your answer is measured to the right of M_2 or measured to the left of M_1. Carefully mark and label this point on the diagram above.

Explanation / Answer

a) let the mass be placed at aa distance x from the mass M2 in between M1 and M2

force by M2 = force by M1

G*M*m / x^2 = G*7M*m/(d - x)^2

7x^2 = x^2 + d^2 - 2dx

6x^2 + 2dx - d^2 = 0

x = -2d + sqrt(4d^2 + 4*6d^2) / 12

= 0.27 d