Home
Class 11
PHYSICS
Two bodies of masses m1 and m2 are initi...

Two bodies of masses `m_1` and `m_2` are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance `r` between them is.

Text Solution

Verified by Experts

Let `upsilon_(r)` be the relative velocity of approach of two bodies at distance `r` apart. The reduced mass of
the system of two particles is, `mu = (m_(1) m_(2))/(m_(1) + m_(2))`.
According to law of conservation of mechincal energy.
Decrease in potential energy = increase in K.E.
`0 - (-(Gm_(1) m_(2))/(r)) = (1)/(2) mu upsilon_(r)^(2)`
or `(Gm_(1) m_(2))/(r) = (1)/(2) ((m_(1) m_(2))/(m_(1) + m_(2))) upsilon_(r)^(2)`
or `upsilon_(r) = sqrt((2G (m_(1) + m_(2)))/(r))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • GRAVIATION

    PRADEEP|Exercise CONCEPTUAL PROBLEMS V.|1 Videos

  • GRAVIATION

    PRADEEP|Exercise VERY SHORT ANS. QUESTIONS I.|1 Videos

  • GRAVIATION

    PRADEEP|Exercise CONCEPTUAL PROBLEMS III.|1 Videos

  • BEHAVIOUR OF PERFECT GAS & KINETIC THEORY

    PRADEEP|Exercise Assertion - Reason Type questions|14 Videos

  • KINEMATICS

    PRADEEP|Exercise 1 NCERT Comprehension|4 Videos

Similar Questions

Explore conceptually related problems

Two bodies of mass m_(1) and m_(2) are initially at rest placed infinite distance apart. They are then allowed to move towards each other under mutual gravitational attaction. Show that their relative velocity of approach at separation r betweeen them is v=sqrt(2G(m_(1)+m_(2)))/(r)

Two bodies of masses m_(1) and m_(2) are initially at infinite distance at rest. Let they start moving towards each other due to gravitational attraction. Calculate the (i) ratio of accelerations and (ii) speeds at the point where separation between them becomes r.

Knowledge Check

  • Two objects of masses m and 4m are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If G is the universal gravitaitonal constant, then at separation r

    A
    the total energy of the two objects is zero
    B
    net angular momentum of both the objects is zero about any point
    C
    the total `K.E.` of the objects is `4Gm^(2)//r`
    D
    their relative velocity of approach is
    `((8Gm)/(r ))^(1//2)`

  • Two particles of mass m and M are initially at rest and infinitely separated from each other. Due to mutual interaction, they approach each other. Their relative velocity of approach at a separation d between them, is

    A
    `[(2" Gd")/("M "+" m")]^(1//2)`
    B
    `[(2" G"(M+m))/(d)]^(1//2)`
    C
    `(2" GM"+m)/(d)`
    D
    None of these

  • Two bodies with masses M_(1) and M_(2) are initially at rest and a distance R apart. Then they move directly towards one another under the influence of their mutual gravitational attraction. What is the ratio of the distances travelled by M_(1) to the distance travelled by M_(2) ?

    A
    `(M_(1))/(M_(2))`
    B
    `(M_(2))/(M_(1))`
    C
    `1`
    D
    `1/2`

    • Similar Questions

    Explore conceptually related problems

    Two particles of mass 'm' and 3 m are initially at rest an infinite distance apart. Both the particles start moving due to gravitational attraction. At any instant their relative velocity of approach is sqrt((ne Gm)/d where 'd' is their separation at that instant. Find ne.

    Two particles m_(1) and m_(2) are initially at rest at infinite distance. Find their relative velocity of approach due to gravitational attraction when their separation is d.

    Two particles of masses m and M are initially at rest at an infinite distance part. They move towards each other and gain speeds due to gravitational attracton. Find their speeds when the separation between the masses becomes equal to d .

    Two objectes of mass m and 4m are at rest at and infinite seperation. They move towards each other under mutual gravitational attraction. If G is the universal gravitational constant. Then at seperation r

    Two objects of massses m and 4 m are at rest at infinite separtion they move twoards each other under mutula gravitonal attraction then at a separation r which of the following is true ?

    Home
    Profile