First slide

Viscosity

Question

A spherical steel ball released at the top of a long column of glycerine of length l, falls through a distance l/2 with accelerated motion and the remaining distance l/2 with uniform velocity. Let $t_{1}$ and $t_{2}$ denote the times taken to cover the first and second half and $W_{1}$ and $W_{2}$ the work done against viscous force in the two halves, then

Moderate

A

$t_{1} < t_{2}$ , $W_{1} > W_{2}$
B

$t_{1}$ > $t_{2}$ , $W_{1}$ < $W_{2}$
C

$t_{1}$ = $t_{2}$ , $W_{1}$ = $W_{2}$
D

$t_{1}$ > $t_{2}$ , $W_{1 =} W_{2}$

Solution

initially as it starts from rest and moves with decreasing acceleration it takes more time for the first half but work done against viscous force will be maximum in the second half as it cross the distance with maximum velocity and viscous force is proportional to velocity.

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