Question

In vacuum on the earth surface, all freely falling bodies:
A) Have the same speed
B) Have the same velocity
C) Have the same force
D) Have the same acceleration

Answer 1

Hint: The motion of any moving object is given by Newton’s second law of motion, which gives,\[{F = m}\times {a}\]. Also for a freely falling body, gravity is the only force acting upon it.

Formulae used:
\[\begin{align}
  & {1}{. F = }\dfrac{{GMn}}{{{{r}}^{{2}}}} \\
 & 2.{ F = m}\times {a} \\
\end{align}\]

Complete step by step solution:
According to Newton's universal law of gravitation force acting on the body is given by
\[{F = }\dfrac{{GMn}}{{{{r}}^{{2}}}}\]
Where m is mass of bodies, which every different body is having different from others hence force acting on different bodies will be different. G is the Universal Gravitational Constant (\[{G=6}{.672 }\!\!\times\!\!{ 1}{{{0}}^{{-11}}}{N}{{{m}}^{{2}}}{/k}{{{g}}^{{2}}}\])
Also we know according to newton’s second law of motion, \[{F = m}\times {a}\] so acceleration is \[\dfrac{{Force}}{{Mass}}={ }\dfrac{{GM}}{{{{r}}^{{2}}}}\] ​, this is independent of the mass of the body or type of the body.
Also, speed or velocity depends on time for which it is accelerated because acceleration is the same which is equal to acceleration due to gravity

Thus option D is correct.

Additional information:
The remarkable observation for all free fall bodies was first proposed by Galileo Galilei with help of an experiment by using a ball on an inclined plane to determine the relationship between the time and distance travelled.

Note: All objects, regardless of size or shape or weight free fall with the same acceleration which is equal to gravitational acceleration ‘g’. For a free falling body, the net external force is equal to \[{F= m}\times g\], which is equal to weight of the body \[{(W = m}\times {g)}\].