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Question: A coaxial cylinder made of glass is immersed in liquid of surface tension ‘S’. Radius of inner and o...

A coaxial cylinder made of glass is immersed in liquid of surface tension ‘S’. Radius of inner and outer surface of cylinder are R1 and R2 respectively. Height till which liquid will rise is (Density of liquid is r)-

A

2SR2ρg\frac{2S}{R_{2}\rho g}

B

2SR1ρg\frac{2S}{R_{1}\rho g}

C

S(R2−R1)ρg\frac{S}{(R_{2} - R_{1})\rho g}

D

2S(R2−R1)ρg\frac{2S}{(R_{2} - R_{1})\rho g}

Answer

2S(R2−R1)ρg\frac{2S}{(R_{2} - R_{1})\rho g}

Explanation

Solution

Net upward force

= 2p R2S + 2pR1 S contact angle = 00

\ Capillary rise is given by

h = 2πS(R1+R2)π(R22−R12)ρg\frac{2\pi S(R_{1} + R_{2})}{\pi(R_{2}^{2} - R_{1}^{2})\rho g}

= 2S(R2−R1)ρg\frac{2S}{(R_{2} - R_{1})\rho g}