A) \[\sqrt{2}\]
B) 2
C) \[2\sqrt{2}\]
D) none of these
Correct Answer: B
Solution :
The effective acceleration of a bob in water \[=\,\,\,g'\,\,=\,\,g\,\left( 1-\frac{\sigma }{\rho } \right)\] where \[\sigma \,\,and\,\,\rho \] are the density of water and the bob respectively. Since the period of oscillation of the bob in air and water are given as \[T=2\pi \,\sqrt{\frac{l}{g}}\] and \[T'=2\pi \,\sqrt{\frac{l}{g'}}\] \[\therefore \,\,\,\,\frac{T}{T'}\,\,=\,\sqrt{\frac{g'}{g}}\,\,=\,\,\sqrt{\frac{g(1-\sigma /\rho )}{g}}\] \[=\,\,\,\,\sqrt{1-\frac{\sigma }{\rho }}\,\,=\,\,\sqrt{1-\frac{1}{\rho }}\] \[Putting\,\,\frac{T}{T'}\,\,=\,\,\frac{1}{\sqrt{2}},\,\,we\,\,obtain,\,\,\frac{1}{2}=1-\frac{1}{\rho }\] \[\Rightarrow \,\,\,\,\,\rho =2\]
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