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A stone is dropped from a height equal t...

A stone is dropped from a height equal to `3R`, above the surface of earth. The velocity of stone on reaching the earth's surface is

A

`sqrt(g R/2)`

B

`sqrt(3/2 gR)`

C

`sqrt(2gR)`

D

`sqrt(gR)`

Text Solution

Verified by Experts

The correct Answer is:
B
`1/2mv^(2)=((mg)Rh)/(R+h)=((mg)R(nR))/(R+nR)`
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Knowledge Check

  • A stone is dropped from a height equal to nR , where R is the radius of the earth, from the surface of the earth. The velocity of the stone on reaching the surface of the earth is

    A
    `sqrt((2g(n+1)R)/n)`
    B
    `sqrt((2gR)/(n+1))`
    C
    `sqrt((2gnR)/(n+1))`
    D
    `sqrt(2gnR)`

  • A particle falls on earth : (i) from infinity. (ii) from a height 10 times the radius of earth. The ratio of the velocities gained on reaching at the earth's surface is :

    A
    `sqrt(11) : sqrt(10)`
    B
    `sqrt(10) : sqrt(11)`
    C
    `10 : 11`
    D
    `11 : 10`

  • A stone of mass "m" initially at rest and dropped from a height "h" strikes the surface of the earth with a velocity "v". If the gravitational force acting on the stone is W , then which of the following identities is correct ?

    A
    `mv - mh = 0`
    B
    `.^(1)//_(2) mv^(2) - Wh^(2) = 0`
    C
    `.^(1)//_(2) mv^(2) - Wh = 0`
    D
    `.^(1)//_(2) mv^(2) - mh = 0`

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