MHT CET · Physics · Mechanical Properties of Fluids

When one end of the capillary is dipped in water, the height of the water column is $h$ . The upward force of $105 dyne$ due to surface tension is balanced by the force due to the weight of the water column. The inner circumference of the capillary is (Surface tension of water $= 7 \times 10^{- 2} N m^{- 1})$

A $1.5 cm$
B $2 cm$
C $2.5 cm$
D $3 cm$

Verified Solution

Answer & Solution

Correct Answer

(A) $1.5 cm$

Step-by-step Solution

Detailed explanation

F = 105 d y n e = 105 \times 10^{- 5} N

T = 7 \times 10^{- 2} N m^{- 1}

2 π r T = F

2 π r = \frac{F}{T} = \frac{105 \times 10^{- 5}}{7 \times 10^{- 2}}

= 15 \times 10^{- 3} m

= 1.5 \times 10^{- 2} m

= 1.5 cm

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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When one end of the capillary is dipped in water, the height of the water column is h. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of the water column. The inner circumference of the capillary is (Surface tension of water =7×10-2 N m-1)

Step-by-step Solution