Question
Eight equal drops of water are falling through air with a steady speed of 10 ~cm / s . If the drops coalesce, the new velocity is:
BITSAT
Physics
Mechanical Properties of Fluids
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Physics Question (2023) — Solution
Options
- A. 10 ~cm / s
- B. 40 ~cm / s
- C. 16 ~cm / s
- D. 5 ~cm / s
Answer
B. 40 ~cm / s
Step-by-step solution
Let r be the radius of small drops of water. R = radius of big drop formed as volume remain same. 8 . 4 3 r ^3- 4 3 R ^3 R =2 r Terminal velocity, aligned & v _ T = 2 9 ( - ) r ^2 ~g \\ & v _ T r ^2 \\ & v _1 v _2 = ( r R )^2 \\ & 10 v _2 = ( 1 2 )^2 ( v _1=10 ~cm / s given ) \\ & v _2=40 ~cm / s aligned
Related: Physics — Mechanical Properties of Fluids · All PYQ Banks