Home
Class 11
PHYSICS
A planet revolves about the sun in an el...

A planet revolves about the sun in an elliptical orbit of semi-major axis `2xx10^(12) m`. The areal velocity of the planet when it is nearest to the sun is `4.4xx10^(16) m//s`. The least distance between the planet and the sun is `1.8xx10^(12) m//s`. The minimum speed of the planet in `km//s` is `10 K`. determine the value of `K`.

Text Solution

Verified by Experts

The correct Answer is:
4
Area covered by line joining planet and the sun in time `dt` is `ds=1/2X^(2)d theta`, area velocity `=(dS)/(dt)=1/2X^(2)(d theta)/(dt)=1/2X^(2)omega` where `X=` distance between planet and sun and `omega=` angular speed of planet about sun. from kepler's second law areal velocity of planet is constant. at farthest position
`A=(dS)/(dt)=1/2(2R-r)^(2)=1/2(2R-r)[(2R-r)omega]`
`=1/2(2R-r)v_(B)` or `v_(B)=(2A)/(2R-r)` least speed, Using values `v_(B)=40 km//s `thus, `K=4`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • GRAVITATION

    NARAYNA|Exercise LEVEL-VI|42 Videos

  • GRAVITATION

    NARAYNA|Exercise ILLUSTRATION|49 Videos

  • GRAVITATION

    NARAYNA|Exercise LEVEL-II (H.W)|32 Videos

  • FRICTION

    NARAYNA|Exercise Passage type of questions I|6 Videos

  • KINETIC THEORY OF GASES

    NARAYNA|Exercise LEVEL-III(C.W)|52 Videos

Similar Questions

Explore conceptually related problems

A planet revolves around the sun in elliptical orbit of semimajor axis 2 × 10^(12 ) m. The areal velocity of the planet when it is nearest to the sun is 4.4 × 10^(16) m^(2)/ /s . The least distance between planet and the sun is 1.8 × 10^(12) m. Find the minimum speed of the planet in km/s.

The time taken by the earth to complete one revolution around the Sun is 3.156xx10^(7)s. The distance between the earth and the Sun is 1.5xx10^(11)m . Find the speed of revolution of the earth.

Knowledge Check

  • A planet of mass m is moving around the sun in an elliptical orbit of semi-major axis a :

    A
    The total mechanical energy of the planet is varying periodically with time
    B
    The total energ of the planet is constant and equals `- (GmM_(s))/(2a), N_(s)` is mass of sun
    C
    Total mechanical energy of the planet is constant and equals `- (GmM_(s))/(a), M_(2)` is mass of sun
    D
    Date is insufficient of arrice at a conclusion

  • A planet revolves about the sun in elliptical orbit. The arial velocity ((dA)/(dt)) of the planet is 4.0xx10^(16) m^(2)//s . The least distance between planet and the sun is 2xx10^(12) m . Then the maximum speed of the planet in km//s is -

    A
    `10`
    B
    `20`
    C
    `40`
    D
    None of these

  • The earth revolves about the sun in an elliptical orbit with mean radius 9.3xx10^(7) m in a period of 1 year. Assuming that there are no outside influences

    A
    The earth's kinetic energy remains constant
    B
    The earth's angular momentum remains constant
    C
    The earth's potential energy remains constant
    D
    All are correct

    • Similar Questions

    Explore conceptually related problems

    The time taken by the earth to complete one revolution around the sun is 3.156 xx 10^(7) s . The distance between the earth and the sun is 1.5 xx 10^(11) m. Find the speed of revolution of the earth.

    A planet of mass m is revolving around the sun in an elliptical orbit. The minimum and maximum distances of the planet from the sun are s_(1) and s_(2) . Derive the relation between time period of the planet in terms of s_(1) and s_(2) .

    A planet of mass m is revolving round the sun (of mass M_(s ) in an elliptical orbit. If vecv is the velocity of the planet when its position vector from the sun is vecr , then areal velocity of the positon vector of the planet is :

    The distance of two planets from the sun are 10^(13) and 10^(12) m respectively. The ratio of the periods of the planet is

    A planet of mass m is revolving round the sun (of mass M_(a) ) in an ellipticla orbit. If vecv is the veclotiy of the planet when its positioni vector from the sun is vecr , then areal velocity of the planet is

    Home
    Profile