Question

Two spheres of the same material but of radii 0.01m and 0.02m are dropped one by one in the same viscous fluid. Their terminal velocities respectively will be in the ratio:​

Answer 1

Answer:

I think this answer should be helpful

Answer 2

Answer:

Their terminal velocities 1:9  respectively.

Explanation:

Step 1: Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. It is observed when the sum of drag force and buoyancy is equal to the downward gravity force acting on the object. The acceleration of the object is zero as the net force acting on the object is zero.

Step 2: Terminal velocity is the constant speed an object acquires after falling through fluid, like air. It occurs when the sum of the buoyant force and the drag force equals the force due to gravity. The terminal velocity is the highest velocity during the object's fall.

Step 3: Terminal velocity

$\quad \mathrm{v}=\frac{2 g r^2(p-\sigma)}{9 \eta}$

where $\eta$ and $\rho$ is the viscosity of liquid and density of material of sphere, respectively

$\Rightarrow \mathrm{v} \propto \mathrm{r}^2$

Given: $r_1=R \quad r_2=3 R$

Thus ratio of velocities

$\frac{\mathrm{v}_1}{\mathrm{v}_2}=\frac{\mathrm{r}_1^2}{\mathrm{r}_2^2}=\frac{\mathrm{R}^2}{9 \mathrm{R}^2}=\frac{1}{9}$

$\Longrightarrow \mathrm{v}_1=\mathrm{v}_2=1: 9$

Hence, Their terminal velocities 1:9  respectively.

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