A) 289\[\omega \]
B) 17\[\omega \]
C) 8\[\omega \]
D) 2\[\omega \]
Correct Answer: B
Solution :
The body will appear weightless only when the centripetal force equals the weight of the body. \[\therefore \] \[\frac{m{{v}^{2}}}{R}=mg\] Since, \[v=R\,\omega \] \[\therefore \] \[\frac{m\,{{(R\omega )}^{2}}}{R}=mg\] \[\Rightarrow \] \[mR{{\omega }^{2}}=mg\] \[\Rightarrow \] \[\omega =\sqrt{\frac{g}{R}}\] Standard value \[(\omega )\] at present is \[\omega =\frac{2\pi }{T}=\frac{2\pi }{86400}rad\,{{s}^{-1}}\] \[=7.3\times {{10}^{-5}}rad\,{{s}^{-1}}\] and \[\omega =\sqrt{\frac{g}{R}}\] \[=\sqrt{\frac{9.8}{6.4\times {{10}^{6}}}}=1.2\times {{10}^{-3}}\] \[\therefore \] \[\omega \approx 17\,\omega \].
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