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A rubber ball of mass 10 gram and volume...

A rubber ball of mass 10 gram and volume `15 cm^3` is dipped in water to a depth of 10m. Assuming density of water uniform throughtout the depth, find (a) the ac celeration of the ball, and (b) the time taken by it to reach the surface if it is relased from rest. `(Take g =980 cm//s^2)`

Text Solution

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the maximum buoyant force on the ball is `F_(B)=Vrho_(w)g=15xx1xx980"dyne"=14700"dyne"`
The weight of the ball is mg `=10xxg=10xx980=9800"dyne"`
the net upward force `F=(15xx980-10xx980)"dyne"=5xx980"dyne"=4900"dyne"`
(a). Therefore, acceleration of the ball upward `a=(F)/(m)=(5xx980)/(10)=490cm//s^(2)=4.9m//s^(2)`
(b). Time taken by it reach the surface is `t=sqrt((2h)/(a))=sqrt((2xx10)/(4.9))s=2.02s`
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