JEE MAIN - Physics (2019 - 10th April Morning Slot - No. 21)
The ratio of surface tensions of mercury and
water is given to be 7.5 while the ratio of thier
densities is 13.6. Their contact angles, with
glass, are close to 135° and 0°, respectively. It
is observed that mercury gets depressed by an
amount h in a capillary tube of radius r1, while
water rises by the same amount h in a capillary
tube of radius r2. The ratio, (r1/r2), is then close
to :
2/5
2/3
3/5
4/5
Explanation
$$h = {{2{S_1}\cos \theta } \over {{r_1}{\rho _1}g}}$$
$$h = {{2{s_2}\cos {\theta _2}} \over {{r_2}{\rho _2}g}}$$
$$ \Rightarrow {{{r_1}} \over {{r_2}}} = {2 \over 5}$$
$$h = {{2{s_2}\cos {\theta _2}} \over {{r_2}{\rho _2}g}}$$
$$ \Rightarrow {{{r_1}} \over {{r_2}}} = {2 \over 5}$$
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