An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension $S$ . The force required to pull the ring away from the liquid surface is

2 π (\sqrt{a_{1} b_{1}} + \sqrt{a_{2} b_{2}}) S

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π (a_{1} + b_{1} + a_{2} + b_{2}) S

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π (\frac{a_{1} + a_{2}}{2} + \frac{b_{1} + b_{2}}{2}) S

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\sqrt{2} π (\sqrt{a_{1} b_{1}} + \sqrt{a_{2} b_{2}}) S

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Solution

The correct option is A $2 π (\sqrt{a_{1} b_{1}} + \sqrt{a_{2} b_{2}}) S$
Internal mean radius $r_{1} \sqrt{a_{1} b_{1}}$
Internal circumfefence of ring = $2 π r_{1} = r_{1} \sqrt{a_{1} b_{1}}$
external mean radius $r_{2} \sqrt{a_{2} b_{2}}$
external circumfefence of ring = $2 π r_{2} = r_{2} \sqrt{a_{2} b_{2}}$
Thus force required = $2 π (\sqrt{a_{1} b_{1}} + \sqrt{a_{2} b_{2}}) S$

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Similar questions

A ring of external and internal radii $r_{1}$ and $r_{2}$ just touches the horizontal surface of a liquid of surface tension $σ$ . The force required to pull the ring away from the surface is

Q. A ring having radius

2.5 cm

and mass

10 gram

floats on a liquid surface having surface tension

0.06 N/m

. Find force required to just lift the ring from liquid surface.

Q. Assertion :Consider

D = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

Let

B_{1}, B_{2}, B_{3}

be the co-factors of

b_{1}, b_{2}

, and

b_{3}

respectively, then

a_{1} B_{1} + a_{2} B_{2} + a_{3} B_{3} = 0

Reason: If any two rows (or columns) in a determinant are identical then value of determinant is zero.

Q. A ring having radius

2.5 cm

and mass

10 gram

floats on a liquid surface having surface tension

0.06 N/m

. Find force required to just lift the ring from liquid surface.

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An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension S. The force required to pull the ring away from the liquid surface is

The correct option is A 2π(√a1b1+√a2b2)SInternal mean radius r1√a1b1Internal circumfefence of ring = 2πr1=r1√a1b1external mean radius r2√a2b2external circumfefence of ring = 2πr2=r2√a2b2Thus force required = 2π(√a1b1+√a2b2)S

An elliptically shaped ring of dimensions shown in figure just touches, the horizontal surface of a liquid of surface tension $S$ . The force required to pull the ring away from the liquid surface is