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Two small bodies of masses 10 kg and 20 ...

Two small bodies of masses 10 kg and 20 kg are kept a distnce 1.0 m apart and released. Assuming that only mutual gravitational force are acting, find the speeds of the particles when the separation decreases to 0.5 m.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`K_(i) + U_(i) = K_(f) + U_(f)`
`underset(10 kg)overset(2V)(rarr)` `underset(20 kg)overset(V)(larr)`
`:. 0 - (Gm_(1)m_(2))/(r_(i)) = (1)/(2) xx 10 (2 nu)^(2) + (1)/(2) xx 20 nu^(2)`
`-(Gm_(1)m_(2))/(r_(f))`
`:. nu= sqrt((Gm_(1)m_(2))/(39)((1)/(r_(f)) - (1)/(r_(f)))`
`= sqrt((6.67 xx 10^(-11)xx 10 xx 20)/(30)((1)/(0.5) - (1)/(1)))`
`= 2.1 xx 10^(-5) m//s`
and `2 nu = 4.2 xx 10^(-5) m//s`
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Knowledge Check

  • Two bodies of masses 50 kg and 100 kg are at a distance 1m apart. The intensity of gravitational field at the mid-point of the line joining them is (in joules)

    A
    100G
    B
    150G
    C
    50G
    D
    200G

  • Two bodies of masses 10 kg and 100 kg are seperated by a distance of 2 m. The gravitational potential at the mid-point of the line joining the two bodies is:

    A
    `-7.3 xx 10^(-7) J//kg`
    B
    `-7.3 xx 10^(-8) J//kg`
    C
    `-7.3 xx 10^(-9) J//kg`
    D
    `-7.3 xx 10^(-6) J//kg`

  • Two bodies of masses 2kg and 4 kg are moving with velocities 20 m/s and 10m/s towards each other due to mutual gravitational attraction . What is the velocity of their centre of mass ?

    A
    `5.3 "ms"^(-1)`
    B
    `6.4 "ms"^(-1)`
    C
    Zero
    D
    `8.1"ms"^(-1)`