A new planet is discovered that has twice the Earth\'s mass and twice the Earth\

Question

A new planet is discovered that has twice the Earth's mass and twice the Earth's radius. On the surface of this new planet a person who weights 500 N on Earth would experience a gravitational force of 125 N 250 N 500 N 1000 N 2000 N The cart of mass 10 kg shown above moves Without friction loss on level table A 10 N force pills on the cart horizontally to the right. At the same time, a 30. N force at an angle of 60degree above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart? 0.5 m/s^2 1.6 m/s^2 2.0 m/s^2 2.5 m/s^2 2.6 m.s^2 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? 16 w 4 w w w 1/16 W

Explanation / Answer

(4). Accleration due to gravity on earth g = GM/R 2

Accleration due to gravity on new planet g ' = GM ' /R ' 2

                                                                     = G(2M)/(2R) 2

                                                                     = 2GM / 4R 2

                                                                    = (1/2)GM/R 2

                                                                    = g / 2

Weight on new planet W = m(g/2)

Weight on earth W ' = mg

                                 = (500N)

Therefore weight on new planet W= mg / 2

                                                      = 500 N / 2

                                                      = 250 N

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