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A body attains a height equal to the rad...

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))`

Text Solution

Verified by Experts

The correct Answer is:
A
Applying conservation of mechanical energy we get,
`(1)/(2)mv^(2)=(mgh)/(1+h//R)`
Putting h = R, we get
`v=sqrt(gR)=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 is was projected is

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

  • 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))`

  • Statement-1 : A body released from a height equal to the radius (R ) of the earth. The velocity of the body when it strikes the surface of the earth will be sqrt(2 g R) . Statement -2 : As upsilon^(2) = u^(2) + 2 as.

    A
    Statement -1 is true , Statement -2 is true , Statement-2 is a correct explanation of Statement -1.
    B
    Statement -1 is true , Statement-2 is true , Statement-2 is a correct explanation of Statement-1.
    C
    Statement-1 is true , Statement-2 is false.
    D
    Statement-1 is false , Statement-2 is true.

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