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A body projected from the surface of the...

A body projected from the surface of the earth attains a height equal to the radius of the earth. The velocity with which the body was projected is

A

`sqrt((2GM)/( R))`

B

`sqrt((GM)/( R))`

C

`sqrt((3GM)/( R))`

D

`sqrt((5GM)/(4R))`

Text Solution

Verified by Experts

The correct Answer is:
B
Applying the principle of conservation of energy,
`E_("surface of the earth")=E_("at a height h")` equal to R
`(1)/(2)mv^(2)-(GMm)/(R )=(1)/(2)m(0)^(2)-(GMm)/(R+R)`
[`because` The velocity of the highest point = 0]
`therefore (1)/(2)mv^(2)=(GMm)/(R )-(GMm)/(2R)=(GMm)/(2R)`
`v^(2)=(GM)/(R )` or `v=sqrt((GM)/(R ))`
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Knowledge Check

  • A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is

    A
    `sqrt((GM)/(R))`
    B
    `sqrt((2GM)/(R))`
    C
    `sqrt((1)/(4)(GM)/(R))`
    D
    `sqrt((GM)/(2R))`

  • A body attains a height equal to the radius of the earth. the velocity of the body with which is was projected is

    A
    `sqrt((GM)/(R))`
    B
    `sqrt((2 GN)/(R))`
    C
    `sqrt((5)/(4)(GM)/(R))`
    D
    `sqrt((3 GM)/(R))`

  • The velocity with which a body should be projected from the surface of the earth such that it reaches a maximum height equal to 5 times radius R fo the earth is (M is mass of the earth )

    A
    `sqrt((3GM)/(5R))`
    B
    `sqrt((4GM)/(3R))`
    C
    `sqrt((4GM)/(5R))`
    D
    `sqrt((5GM)/(3R))`

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