Question

The ratio of distances traversed in successive intervals of time when a body falls freely under gravity from certain height is 

(a) 1 : 2 : 3 

(b) 1 : 5 : 9 

(c) 1 : 3 : 5 

(d) √1 : √2: √3

Answer 1

Correct option (c) 1 : 3 : 5

Explanation:

As we know, distance traversed in n^th second

S_n = u + 1/2a(2n - 1)

Here, u = 0, a = g

∴ S_n = 1/2g(2n - 1)

Distance traversed in 1^st second i.e., n = 1

S₁ = 1/2g(2 x 2 - 1) = 1/2g

Distance traversed in 2nd second i.e., n = 2

S₂ = 1/2g(2 x 2 - 1) = 3/2g

Distance traversed in 3rd second i.e., n = 3

S₃ = 1/2g(2 x 3 - 1) = 5/2g

∴ S₁ : S₂ : S₃ = 1/2g : 3/2g : 5/2g = 1 : 3 : 5