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Two bodies of masses 2 m and m have thei...

Two bodies of masses 2 m and m have their K.E. in the ratio 8 : 1, then their ratio of momenta is

A

`1:1`

B

`2:1`

C

`4:1`

D

`8:1`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • Two bodies of masses 2m and m have their K.E. in the ratio 8 : 1, then their ratio of momenta is

    A
    `1:1`
    B
    `2:1`
    C
    `4:1`
    D
    `8:1`

  • Two bodies of masses 3 m and m have their K.Einh 27:1 then the ratio of the momentum is

    A
    `9:1`
    B
    `1:9`
    C
    `1:3sqrt3`
    D
    `1:1`

  • Two bodies of masses m and 4 m are moving with equal K.E. The ratio of their linear momentums is

    A
    `4:1`
    B
    `1:1`
    C
    `1:2`
    D
    `1:4`

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    Two bodies of masses m_1 and m_2 have the same linear momentum. What is the ratio of their kinetic energies?

    Two bodies of masses m_1 and m_2 have equal kinetic energies. What is the ratio of their linear momenta?

    Relation between kinetic energy and momentum Let us consider a body of mass 'm' having a velocity 'v', then momentum of the body P = mass xx velocity P = m xx v rArr v = (P)/(m) " "...(1) From definition, kinetic energy (K.E) of the body K.E = (1)/(2) mv^(2)" "...(2) Now putting the value of (1) in (2) we have K.E = (1)/(2)m ((P)/(m))^(2) K.E. = (1)/(2)m (P^(2))/(m^(2)) = (1)/(2) (P^(2))/(m) = (P^(2))/(2m)" "...(3) Thus we can write P^(2) = 2m xx K.E rArr P = sqrt(2m xx K.E) Thus momentum = sqrt(2 xx "mass" xx "kinetic energy") Two bodies masses 1 kg and 4 kg having equal kinetic energies. The ratio of their momentum is

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