Question

A spherical solid ball of volume $V$ and mass $m$ is falling in a viscous liquid with a terminal speed $V_0$. In this condition, which of the following statements is wrong? (neglect buoyant force)

• A. Acceleration of ball is zero.
• B. Weight is balanced by viscous force of liquid.
• C. Loss of potential energy converts into kinetic energy.
• D. Rate of loss of potential energy is equal to power supplied by viscous force.

Answer 1

The correct option is C Loss of potential energy converts into kinetic energy.

Let the viscous force be $f_v$.
As the ball moves with constant terminal speed, acceleration of the ball is zero.
$\therefore F_{net}=0$ and
$F_{net}=mg-f_v$
$\Rightarrow mg=f_v$
Also, the net power supplied to the ball is zero.
i.e., $P_{net}=0$
$\Rightarrow (mg-f_v)V_0=0$
$\Rightarrow mg{V}_0=f_v{V}_0$
$\therefore$Rate of loss of potential energy $=$ Power supplied by viscous force.
Hence options $a,b$ and $d$ are correct.

The kinetic energy of the ball is not changing, because its speed is constant, hence option $c$ is wrong.