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If a body is to be projected vertically upwards from earth's surface to reach a height of `10R` where `R` is the radius of earth. The velocity required to be si is

A

`sqrt((24)/(11) gr)`

B

`sqrt((22)/(11) gr)`

C

`sqrt((20)/(11) gr)`

D

`sqrt((18)/(11) gr)`

Text Solution

Verified by Experts

The correct Answer is:
C
From law of conservation of energy, we have
`-(GM m)/(R ) + (1)/(2) m upsilon^(2) = - (GM m)/((10 R + R)) + 0 = - (GM m)/(11R)`
or `(1)/(2) upsilon^(2) = (GM)/(R ) - (GM)/(11R) = (10)/(11)(GM)/(R )`
or `upsilon^(2) = (20)/(11) (GM)/(R ) = (20)/(11)g R` or `upsilon = sqrt((20g R)/(11))`
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Knowledge Check

  • A body is to be projected vertically upwards from earth's surface to reach a height of 9R , where R is the radius of earth. What is the velocity required to do so? Given g=10ms^(-2) and radius of earth =6.4xx10^(6)m .

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    B
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    `10.73xx10^(4) ms^(-1)`
    D
    `17.3xx10^(4) ms^(-1)`

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