Question

In a vacuum , which has a greater acceleration while in free fall: a 7kg bowling ball or a 0.007 kg feather?

a) It depends on the air resistance
b) they will have the same acceleration
c) the feather
d) the bowling ball

Answer 1

b) They will have the same accelerationStep-by-step explanation:

The acceleration of an object in free fall is known as the acceleration due to gravity, g, which is due to the attractive force of the Earth's gravitational field on the object. and is given by the following formula;

`g = G * (Mass \ of \ the \ Earth)/((Distance \ between \ the \ object \ and \ the \ center \ of \ the \ Earth)^2)`

`g = G * (M)/(r^2)`

r = R + h

Where;

R = The radius of the Earth

h = The height of the center of the object above Earth's surface

Therefore, due to the large magnitude of R, and the comparatively small magnitude of h, R + h is approximately R, that is R + h ≈ R and R ≈ r, which gives;

`g = G * (M)/(R^2)`

Therefore, given that, the mass of the Earth, M, the radius of the Earth, R and the gravitational constant, G, are all constant, the value of g is therefore, constant for all objects and the value is approximately 9.81 m/s².