Question

Two solid spheres of same material but of mass M and 8M fall simultaneously on a viscous liquid and their terminal velocities are V and nV, then the value of n is

• A. \(16\)
• B. \(8\)
• C. \(4\)
• D. \(2\)

Hint:

Terminal velocity varies as the square of the radius, and the radius scales as the cube root of the mass.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For spheres of the same material, terminal velocity is \(v\propto r^{2}\).

Step 2: Relate Mass and Radius
Mass \(\propto r^{3}\). The mass ratio is \(\frac{8M}{M}=8\), so \(\frac{r_2}{r_1}=8^{1/3}=2\).

Step 3: Calculation
\(\frac{v_2}{v_1}=\left(\frac{r_2}{r_1}\right)^{2}=2^{2}=4\)

Step 4: Compare the options
So \(nV=4V\) and \(n=4\), option (C).

Final Answer:
The value of n is 4. \[ \boxed{\text{(C) }4} \]