TS EAMCET · Physics · Thermal Properties of Matter

A wooden block of density $0.5 g / cc$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 g / cc .$ If the tension of the string is $20 N,$ then the mass of the block is
(Take $g = 10 m / s^{2}$ )

A $1 kg$
B $2 kg$
C $3 kg$
D $0.5 kg$

Verified Solution

Answer & Solution

Correct Answer

(B) $2 kg$

Step-by-step Solution

Detailed explanation

At equilibrium, tension in the string must be equal to apparent weight of the block in liquid, T=WApparent ⇒T=FB-W ⇒T=ρlVg-ρsVg On putting all the corresponding values, we have ⇒20=1000-500V×10 ⇒V=205000=1250 m3 Mass of the block is,…

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 wooden block of density 0.5 g/cc is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density 1 g/cc. If the tension of the string is 20 N, then the mass of the block is(Take g=10 m/s2)

Step-by-step Solution

A wooden block of density $0.5 g / cc$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 g / cc .$ If the tension of the string is $20 N,$ then the mass of the block is
(Take $g = 10 m / s^{2}$ )