Question

Two solid spheres of same material but of mass ' M ' and ' 8 M ' fall simultaneously through a viscous liquid. Their terminal velocities are respectively ' V ' and ' nV '. The value ' n ' is

• A. 2
• B. 4
• C. 8
• D. 16

Hint:

For the same material, mass is proportional to radius cubed, and terminal velocity is proportional to radius squared.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Terminal velocity \(v_t = \dfrac{2r^2(\rho-\sigma)g}{9\eta}\), so \(v_t\propto r^2\) for the same material.

Step 2: Radius Ratio
Mass \(\propto r^3\). Mass ratio \(8M : M\) gives radius ratio \(2:1\).

Step 3: Velocity Ratio
\(\dfrac{v_2}{v_1} = \left(\dfrac{r_2}{r_1}\right)^2 = 2^2 = 4\).

Step 4: Result
\(n = 4\), option B.

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