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The velocity of small ball of mass M and...

The velocity of small ball of mass `M` and density `d_(1)` when dropped a container filled with glycerine becomes constant after some time. If the density of glycerine is `d_(2)`, the viscous force acting on ball is

A

`(Md_(1)g)/(d_(2))`

B

`Mg(1-(d_(2))/(d_(1)))`

C

`(M(d_(1)+d_(2)))/(g)`

D

`Mg(1-(d_(1))/(d_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, ball gains constant velocity
Therefore, net force on the ball = zero
` rArr` Weight of the ball = Buoyant force + Viscous force `(F_(v))`
`impliesMg=(M)/(d_(1))xxd_(2)xxg+F_(v)" "therefore" "F_(v)=Mg(1-(d_(2))/(d_(1)))`
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