Eight identical drops of water are falling through air with a steady velocity | PGMN Solutions

Eight identical drops of water are falling through air with a steady velocity of 12" " cm〖" " s〗^(-1). All the drops merge into a bigger drop. The terminal velocity of the bigger drop is
(A) 36" " cm〖" " s〗^(-1)
(B) 40" " cm〖" " s〗^(-1)
(C) 48" " cm〖" " s〗^(-1)
(D) 60" " cm〖" " s〗^(-1)

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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Mechanical Properties of Fluids
📌 Topic: Viscous Force and Terminal Velocity

🔹 Step 1: Understand the concept of terminal velocity
Terminal velocity is the constant speed a falling object reaches when the force due to gravity is balanced by the resistive force from the fluid, like air.

🔹 Step 2: Know how terminal velocity depends on radius
For a spherical object like a drop falling in a fluid, terminal velocity increases as the square of the radius.

🔹 Step 3: Combine the eight drops into one
When 8 identical drops combine, the volume of the bigger drop becomes 8 times the volume of a single drop. Since volume is proportional to the cube of the radius, the radius of the bigger drop becomes twice that of a single drop.

🔹 Step 4: Apply the terminal velocity relationship
Since terminal velocity is proportional to the square of the radius, and the new radius is twice that of the original, the terminal velocity becomes four times that of the small drop.

✅ Final Answer: (C) 48 cm per second 🚀

🔥 Pro Tip:
When multiple identical drops merge, always remember that the final radius increases with the cube root of the number of drops, and terminal velocity depends on the square of the radius.


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