TS EAMCET · Physics · Mechanical Properties of Fluids

A hollow spherical body of outer and inner radii of $4 cm$ and $2 cm$ respectively floats half submerged in a liquid of density $2.0 g {cm}^{- 3}$ . The density of the material of the sphere is

A $1.02 g {cm}^{- 3}$
B $1.14 g {cm}^{- 3}$
C $1.18 g {cm}^{- 3}$
D $1.24 g {cm}^{- 3}$

Verified Solution

Answer & Solution

Correct Answer

(B) $1.14 g {cm}^{- 3}$

Step-by-step Solution

Detailed explanation

Volume of the material used for making the hollow sphere is, V=43πR3-r3. For a floating body, buoyance force is equal to the weight of the body. Therefore, B=mg⇒ρLV'g=ρSVg⇒ρL×23πR3=ρS×43πR3-r3⇒ρS=1.14 g …

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.

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A hollow spherical body of outer and inner radii of 4 cm and 2 cm respectively floats half submerged in a liquid of density 2.0 g cm-3. The density of the material of the sphere is

Step-by-step Solution

A hollow spherical body of outer and inner radii of $4 cm$ and $2 cm$ respectively floats half submerged in a liquid of density $2.0 g {cm}^{- 3}$ . The density of the material of the sphere is