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A spherical ball is moving with terminal...

A spherical ball is moving with terminal velocity inside a liquid determine the relationship of rate of heat loss with the radius of ball.

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Rate of heat loss`=` power `=F xx v=6pi eta r v xx v =6 pi eta r v^(2)=6p eta r [(2)/(9)(gr^(2)(rho_(0)-rho_(l)))/(eta)]^(2)`
Rate of heat loss `alpha r^(5)`
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Knowledge Check

  • A spherical ball falls through viscous medium with terminal velocity v . If this ball is replaced by another ball of the same mass but half the radius, then the terminal velocity will be (neglect the effect of buoyancy.)

    A
    `v`
    B
    `2v`
    C
    `4v`
    D
    `8v`

  • A ball of mass m inside a smooth spherical shell of radius R with velocity sqrt(2qR) at A What is the direction of force acting on the ball, when it reaches B ?

    A
    BP
    B
    BQ
    C
    BR
    D
    BS

  • A metal ball falls through water with terminal velocity 20 ms^(-1) . When the ball is allowed to fall through vacuum, then

    A
    Terminal velocity is 30 `ms^(-1)`
    B
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    C
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    D
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