Question

if the ratio of kinetic enegies is 2:1 and momemtum is equal, find the ratio of their masses.

Answer 1

Answer:

k.E =momentum square per 2m

ratio 1:2

Answer 2

Ratio of their masses is 1:2

Explanation:

• Momentum of any body is given as the product of mass of the body and velocity of the body that is it given as motion of body
• Whereas kinetic energy is the energy possessed by its motion

Suppose, mass of one object = m₁

mass of another object = m₂

velocity of one object = v₁

velocity of another object = v₂

momentum of one body = P₁ = m₁v

momentum of another object = P₂ = m₂v₂

Kinetic energy of one object = $\frac{1}{2} m_{1} v_{1} ^{2}$

Kinetic energy of another object = $\frac{1}{2} m_{2} v_{2} ^{2}$

Given, ratio of kinetic energy = 2:1

Momentum of the bodies are equal P₁= P₂

Kinetic energy can also be written as = $\frac{1}{2m } (mv)^{2}$ = $\frac{1}{2m } P^{2}$

=> $\frac{\frac{P_{1}^{2} }{2m_{1} } }{\frac{P_{2}^{2} }{2m_{2} } }$   = 2:1

=> $\frac{m_{2} }{m_{1} }$ = 2:1

=> m₁ : m₂ = 1:2

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