Question

The acceleration due to gravity at the north pole of Neptune is approximately 10.7m/s2. Neptune has mass 1026kg and radius 25000km and rotates once around its axis in a time of about 16h.
Part A

What is the gravitational force on an object of mass 5.5kg at the north pole of Neptune?

Part B

What is the apparent weight of this same object at the Neptune's equator? (Note that Neptune

Answer 1

Answer:

(A) Force on the object will be 58.85 N

(B) Apparent weight will be equal to 57.21 N

Explanation:

We have given mass of Neptune m = 1026 kg

Radius R = 25000 Km

Time period = 16 hour

We know that 1 hour = 3600 sec

So 16 hour = 16×86400 = 57600 sec

Acceleration due to gravity at north pole of Neptune $g=10.7m/sec^2$

(A) Mass of the object m = 5.5 kg

So gravitational force on the object $F_g=mg=5.5\times 10.7=58.85N$

(B) Velocity will be equal to $v=\frac{2\pi R}{T}=\frac{2\times 3.14\times25000\times 1000}{57600}=2725.694m/sec$

Apparent weight of the object will be equal to $w=f_g-\frac{mv^2}{r}$

$W=58.85-\frac{5.5\times (2725.694)^2}{25000\times 1000}=57.21N$