TS EAMCET · Physics · Mechanical Properties of Fluids

A solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force and gravitational force acting on it are \(\mathrm{F}_{\mathrm{v}}, \mathrm{F}_{\mathrm{B}}\) and \(\mathrm{F}_{\mathrm{W}}\) respectively. Then the correct relation between them is

A \(\mathrm{F}_{\mathrm{B}}>\mathrm{F}_{\mathrm{V}}=\mathrm{F}_{\mathrm{W}}\)
B \(\mathrm{F}_{\mathrm{W}}=\mathrm{F}_{\mathrm{V}}+\mathrm{F}_{\mathrm{B}}\)
C \(\mathrm{F}_{\mathrm{B}}=\mathrm{F}_{\mathrm{W}}+\mathrm{F}_{\mathrm{V}}\)
D \(\mathrm{F}_{\mathrm{V}}=\mathrm{F}_{\mathrm{B}}+\mathrm{F}_{\mathrm{W}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\mathrm{F}_{\mathrm{W}}=\mathrm{F}_{\mathrm{V}}+\mathrm{F}_{\mathrm{B}}\)

Step-by-step Solution

Detailed explanation

Gravitational force, \(\left(\mathrm{F}_{\mathrm{w}}\right)=\) Viscous Force \(\left(\mathrm{F}_{\mathrm{v}}\right)+\) Buoyant Force \(\left(\mathrm{F}_{\mathrm{B}}\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app