Question

2 bodies of masses 2 m and m have their kinetic energy in the ratio of 8:1, then the ratio of their linear momenta is

Answer 1

$\underline{\underline{\red{\sf{Given:}}}}$

• 2 bodies of masses 2m and m have a kinetic energy of ratio 8:1.

$\underline{\underline{\red{\sf{To\:Find:}}}}$

• The ratio of their linear momenta.

$\underline{\underline{\red{\sf{Answer:}}}}$

Given that the ratio of kinetic energy of two bodies is 8:1 and they have masses of 2m and m respectively.

Firstly we know that Momentum = mass×velocity.

★ p = mv ★

Also we know that ,

★ Kinetic energy = ½ mv² ★

So ,let

• Velocity of first body as u.
• Velocity of second body as v .

Kinetic energy of first body = ½ × 2m × u² = mu².

Kinetic energy of 2nd body = ½ × m × v² = mv²/2

On dividing both ,

=> 8/1 = mu²×2/mv².

=> 8/2 = u²/v².

=> 4 = u²/v².

=> u² = 4v².

=> u = 2v .

So ,

• Momentum of first body = mu = m × 2v = 2mv
• Momentum of second body = mv .

Hence required ratio = 2mv:mv = 2:1.

Hence the required ratio is 2:1.