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Two bodies of masses m and 4m are moving with equal kinetic energies. The ratio of their linear momenta will be [1988]
  • a)
    1 : 4
  • b)
    4 : 1
  • c)
    1 : 2
  • d)
    2 : 1
Correct answer is option 'C'. Can you explain this answer?
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Two bodies of masses m and 4m are moving with equal kinetic energies. ...
Hence, 
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Two bodies of masses m and 4m are moving with equal kinetic energies. ...
Solution:

Given: Two bodies of masses m and 4m are moving with equal kinetic energies.

Let us assume that the kinetic energy of each body is K.

To Find: The ratio of their linear momenta.

Let the linear momentum of the first body be p1 and that of the second body be p2.

Formula: The kinetic energy of a body is given by K = (1/2)mv^2, where m is the mass of the body and v is its velocity.

From the formula, we can write the velocity of each body as:

v1 = √(2K/m) and v2 = √(2K/4m) = √(K/m)

Explanation:

Step 1: Calculation of linear momentum of first body

The linear momentum of the first body can be calculated as:

p1 = mv1 = m√(2K/m) = √(2mK)

Step 2: Calculation of linear momentum of second body

The linear momentum of the second body can be calculated as:

p2 = 4mv2 = 4m√(K/m) = 2√(mK)

Step 3: Calculation of ratio of linear momenta

The ratio of the linear momenta of the two bodies can be calculated as:

p1/p2 = (√(2mK))/(2√(mK)) = 1/2

Therefore, the ratio of the linear momenta of the two bodies is 1:2.

Hence, the correct option is (c) 1:2.

Answer: Option (c) 1:2.
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Community Answer
Two bodies of masses m and 4m are moving with equal kinetic energies. ...
KE=p^2/2m .....
as kinetic energy same ....
so mass proportional to squre of momentum...
so .. option c is correct
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