A) 20 cm
B) 4 cm
C) 2 cm
D) 0.2 cm
Correct Answer: C
Solution :
[c] : According to Bernoulli s theorem, \[P+\frac{1}{2}\rho {{v}^{2}}=\]constant. Near the ends, the velocity of liquid is higher so that pressure is lower as a result the liquid rises at the sides to compensate for this drop of pressure. i.e.,\[\rho gh=\frac{1}{2}\rho {{v}^{2}}=\frac{1}{2}\rho {{r}^{2}}{{\omega }^{2}}\] Hence,\[h=\frac{{{r}^{2}}{{\omega }^{2}}}{2g}=\frac{{{r}^{2}}{{(2\pi \upsilon )}^{2}}}{2g}=\frac{2{{\pi }^{2}}{{r}^{2}}{{\upsilon }^{2}}}{g}\] \[=\frac{2\times {{\pi }^{2}}\times {{(0.05)}^{2}}\times {{2}^{2}}}{9.8}\]\[=0.02m=2cm\]
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