A) \[\sqrt{\frac{2h}{g}}\]
B) \[\sqrt{\frac{2h}{g}\,.\,\frac{D}{d}}\]
C) \[\sqrt{\frac{2h}{g}\,.\,\frac{d}{D}}\]
D) \[\sqrt{\frac{2h}{g}}\,\left( \frac{d}{D-d} \right)\]
Correct Answer: D
Solution :
Upthrust ? weight of body = apparent weight \[VDg-Vdg=Vda,\] Where a = retardation of body \ \[a=\left( \frac{D-d}{d} \right)\ g\] The velocity gained after fall from h height in air, \[v=\sqrt{2gh}\] Hence, time to come in rest, \[t=\frac{v}{a}=\frac{\sqrt{2gh}\times d}{(D-d)g}=\sqrt{\frac{2h}{g}}\times \frac{d}{(D-d)}\]
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