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Q.

In a horizontal capillary tube, the rate of capillary flow depends on the surface tension force as well as the viscous force. Lueas and washburn showed that the length (x) of liquid penetration in a horizontal capillary depends on a factor (k) apart from time (t). The factor is given by k=rTcosθ2η12; where r, T, θ and η are radius of the capillary tube, surface tension, contact angle and coefficient of viscosity respectively. If the length of liquid in the capillary grows from zero to x0 in time t0, how much time will be needed for the length to increases from x0 to 4x0.

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a

6t0

b

4t0

c

12t0

d

15t0

answer is D.

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Detailed Solution

One can easily show that dimension of the factor k are: [k] = ML1T12
If x = kta, then a = ½
xt12
Time needed for x to go from zero to x0 is t0
Time for x to grow from zero to 4x0 will be 16t0
 required answer is 15t0

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