Question

A body starts from rest and is acted on by a constant force. The ratio of kinetic energy gained by it in the first five seconds to that gained in the next five-second is:

विकल्प

• 2 : 1

• 1 : 1

• 3 : 1

• 1 : 3

Answer 1

1 : 3

Explanation:

constant force → constant acceleration = a

⇒ `("V"_5 - "V"_0)/"t" = "a" = ("V"_5 - 0)/5` = a = V₅ = 5a

⇒ KE₅ = `1/2 "mv"_5^2 = 25/2 "ma"^2`

`("V"_10 - "V"_0)/"t"` = a ⇒ V₁₀ = 10a

⇒ KE₁₀ = `100/2 "ma"^2`

So KE gained between 5s and 10s  = KE₁₀​ − KE₅ = `75/2 "ma"^2`

KE  gained in 5s = `25/2"ma"^2`

Ratio = `25/75` = 1 : 3