Question

Two identical objects are dropped from rest at the same time. Object A is dropped from twice the height of object B. If there is no air resistance, which statement is true?

None of the answers given is true.

Both objects hit the ground at the same time.

Object A takes twice the time to fall as object B.

Object A takes four times the time to fall as object B.

Answer 1

S = ut + (1 / 2)at^{​​​​​2}

Here, for both objects, the initial velicity is 0.

So,

S = (1 / 2)at^{​​​​​2}

Let the object B is at a height h.

Distance travelled by object B = 2h

Both objects have same acceleration due to gravity.

For object B,

h = (1 / 2)gt_B^{​​​​​2}

For object A,

2h = (1 / 2)g×t_A²

t_{​​​​​​A}^{​​​​​2} = 2×t_B²

t_{​​​​​​A} = √2 × t_{​​​​​​B}

So, none of the answers given is true.