First slide

Viscosity

Question

When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is “a” (just after the release). Then its acceleration when it has acquired 3/5 of maximum velocity is $\frac{x a}{y}$ , find x + y.

Moderate

A

5
B

7
C

9
D

11

Solution

The terminal velocity $V_{f}$ of the ball is attained when net force on the ball is zero.
The viscous force is = $\frac{3}{5} W_{e f f}$
Hence, net force is $W_{e f f} - \frac{3}{5} W_{e f f} = \frac{2}{5} W_{e f f}$
Therefore, the required acceleration is $\frac{2 a}{5}$ .
Here x = 2, y = 5, therefore x + y = 7.

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