Two identical objects A and B fall from rest from different heights to the ground.If object B takes twice as long as A to reach the ground,what is the ratio of the heights from which A and B fell? Neglect air resistance.
A)1 :
B)1 : 2
C)1 : 4
D)1 : 8

Question

Two identical objects A and B fall from rest from different heights to the ground.If object B takes twice as long as A to reach the ground,what is the ratio of the heights from which A and B fell? Neglect air resistance.
A)1 : 
B)1 : 2 
C)1 : 4 
D)1 : 8

Quizplus · Accepted Answer

Let the height of object A be h.
Then, the time taken by object A to reach the ground is given by:
t = sqrt(2h/g)
where g is the acceleration due to gravity.

For object B, the height is 4h (since it falls for twice the time).
So, the time taken by object B is given by:
2t = sqrt(8h/g)

Equating the above two equations and solving for h, we get:
h = 4h/2^2
=> h = h/4

Therefore, the ratio of the heights from which A and B fell is h:(4h) = 1:4.

Two Identical Objects a and B Fall from Rest from Different