Question

When the speed of a ball is doubled its kinetic energy
(a) Remains same
(b) gets doubled(c) Becomes half
(d) becomes 4 times

Answer 1

Answer ⇒ Option (d). 4 times.

Explanation ⇒

Let the Original Velocity, mass and the kinetic energy of the body be v, m and K₁ respectively.

∴ K = 1/2 × mv² -----eq(i)

Now,

If the velocity becomes 2 times of the original, then new velocity = 2v

∴ New Kinetic Energy = 1/2 × m(2v)²

⇒ K₂ = 1/2 × mv² × 4

⇒ K₂ = K₁ × 4 [From eq(i)]

⇒ K₂ = 4K₁

Hence, the kinetic energy becomes 4 times of the original.

Hope it helps.

Answer 2

When the speed of a ball is doubled its kinetic energy (d) becomes 4 times

Momentum is mass X speed.

So, when speed is doubled , momentum ‘ p’ also gets doubled .

p’ = 2p

Kinetic energy is (1/2) ( mv) * v = (1/2) p v

So, when speed is doubled , kinetic energy ‘E” ‘’gets quadrupled .

E’ = 4E

The ratio of p’ to E’ is p’/E’ = 2p/4E =(p/E) /2