A) \[2:9\]
B) \[3:16\]
C) \[1:2\]
D) \[3:2\]
Correct Answer: C
Solution :
Momentum = Mass \[\times \] Velocity =p \[{{v}^{2}}+{{u}^{2}}+2gh\] When \[u=0,\,{{v}^{2}}=2gh\] \[\therefore \] \[v=\sqrt{2gh}\] \[\frac{{{p}_{1}}}{{{p}_{2}}}=\frac{{{m}_{1}}{{v}_{1}}}{{{m}_{2}}{{v}_{2}}}=\left( \frac{2}{3} \right)\frac{\sqrt{2g{{h}_{1}}}}{\sqrt{2g{{h}_{2}}}}\] \[=\frac{2}{3}\sqrt{\frac{{{h}_{1}}}{{{h}_{2}}}}=\frac{2}{3}\times \sqrt{\frac{9}{16}}=\frac{2}{3}\times \frac{3}{4}=\frac{1}{2}\]
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