Problem: Law of Gravity and Weight (1998) 39. An object has a weight W when it i

Question

Problem: Law of Gravity and Weight (1998) 39. An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet? (A) 16W (B) 4W (C) W (D) W Show your work; 4 16 Problem: Law of Gravity and Accel. (1993) 48. The planet Mars has mass 6.4 x 1023 kilograms and radius 3.4 x 106 meters. The acceleration of an object in free-fall near the surface of Mars is most nearly (A) zero (D) 3.7 m/s2 (E) 9.8 m/s2 Show your work: (B) 1.0 m/s2 (C) 1.9 m/s2

Explanation / Answer

here,

the gravitational acceration , g = G * M /R^2

as the distance is increased to 4R

the gravitational acceration , g' = G * M /R'^2

g' = G * M /(4R)^2

g' = g/16

and weight , W = m * g

so, the weight at a distance 4R from the center is (E) W/16

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