The acceleration due to gravity at the north pole of Neptune is approximately 10.7 m/s2. Neptune has mass 1.0 × 1026 kg and radius 2.5 × 104 km and rotates once around its axis in about 16 h. (a) What is the gravitational force on a 5.0-kg object at the north pole of Neptune? (b) What is the apparent weight of this same object at Neptune’s equator? (Note that Neptune’s “surface” is gaseous, not solid, so it is impossible to stand on it.)

Solution Step 1 of 6 In the given problem, the acceleration due to gravity g=10.7m/s is given near north pole for neptune planet with mass M=1× 10 kg with radius r=2.5 × 10 km with time period for one rotation is t= 16 h. Here we need to calculate the gravitational force on m=5 kg object at the north pole and apparent weight of this object at equator. Step 2 of 6 Given data, Acceleration due to gravity g=10.7m/s 2 26 Neptune mass, M=1× 10 kg Radius of neptune , r=2.5 × 10 km Using 1km= 10 m 3 r=2.5 × 10 m Mass of the object, m= 5 kg Time period, t=16 h Using 1hr = 60×60 sec=3600 s t=16× 3600 sec t=57600 sec Angular displacement, = 1 rev Using 1 rev=2 rad = 2 rad To find, The gravitational force on object at the north pole, F= Apparent weight of this object at equator, W= Step 3 of 6 To calculate gravitational force on object at the north pole, Gravitational force will be equal to weight at the north pole, F g mg 2 Substituting m = 5 kg and g=10.7m/s 2 F g5 kg (10.7m/s ) F g53.5 N Therefore, the gravitational force on object at the north pole is 53.5 N.