Question

Consider the following statements A and B and identify the correct answer.

A) The speed acquired by a body when falling in a vacuum for a given time is dependent on the mass of the falling body.

B) A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for $5s$. [$g=10m{s}^{-2}$]

• A. Both A & B are true
• B. A is true but B is false
• C. B is true but A is false
• D. Both A & B are false

Answer 1

The correct option is C B is true but A is false

A) The Kinematic equation: $v=u+at$ shows that the speed of the freely falling body depends on initial velocity u, acceleration a and time t. It does not depend on the mass. Therefore, statement A is false.
B) In general the distance traveled by the stone in some $n^{th}$ second is given by:
$S_n=u+\frac{1}{2}a(2n-1)$
The stone falls freely from rest $\therefore u=0$
Let $n$ be the last second (time stone remains in air). Now distance traveled is iven by:
$S_n=\frac{1}{2}a(2n-1)$
This is also equal to the distance covered in first three seconds. This implies:
$\frac{1}{2}a(2n-1)=ut+\frac{1}{2}a{t}^2=\frac{1}{2}{3}^{2}a=\frac{9}{2}a$
$\Rightarrow 2n-1=9$
$\Rightarrow n=5$
The stone remains in air for 5 sec and hence statement B is true.