Two bodies having masses in the ratio of 3 : 1 possessthe same kinetic energy. The ratio of their linearmomentum isa)1 : 4b)2 : 1c)1 : 3d) Correct answer is option 'D'. Can you explain this answer?

Question

Two bodies having masses in the ratio of 3 : 1 possessthe same kinetic energy. The ratio of their linearmomentum isa)1 : 4b)2 : 1c)1 : 3d)  Correct answer is option 'D'. Can you explain this answer?

Answer

K.E =P^2/2m.K.E1/K.E2=P1^2×m2/P1^2×m1.given that both K.E are equal.then,P1^2/P2^2=m1/m2P1^2/P2^2=3/1.P1/P2=√3:√1=√3:1.....

Answer

We know that K.E. = p^2/2m ...here it is given that both have same k.e. so the ratio of square of momentum will be equal to their masses...therefore p1/p2 = m1/m2 that is under root 3 : 1

Answer

Concept:
When two bodies have different masses but possess the same kinetic energy, their linear momentum will be in a specific ratio. This ratio can be determined using the formula for kinetic energy and linear momentum.

Given:
Mass ratio of the bodies = 3 : 1

Let:
Mass of the first body = 3x
Mass of the second body = x

According to the question:
$$\frac{1}{2} \times 3x \times v^2 = \frac{1}{2} \times x \times v^2$$
(where v is the velocity of both bodies)

Solving the equation:
$$3xv^2 = xv^2$$
$$3 = 1$$
This equation shows that the linear momentum of the first body is three times that of the second body.

Therefore, the ratio of their linear momentum is:
√3 : 1
So, the correct answer is option 'D' which is √3 : 1.

Answer

Option d is correct answer

Answer

D

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