A) \[1\]
B) \[8.5\]
C) \[17\]
D) \[34\]
Correct Answer: C
Solution :
Earth rotates about its own axis in\[24\,\,h\]. So, \[T=24\times 60\times 60\,\,s\] So, angular speed of earth about its own axis \[\omega =\frac{2\pi }{T}=\frac{2\pi }{24\times 60\times 60}rad/s\] At equator,\[g'=g-{{R}_{e}}\omega {{'}^{2}}\] or \[0=g-{{R}_{e}}\omega {{'}^{2}}\] or \[\omega '=\sqrt{\frac{g}{{{R}_{e}}}}=\frac{2\pi }{84.6\times 60}\] \[\therefore \] \[\frac{\omega '}{\omega }=\frac{24\times 60\times 60}{84.6\times 60}\approx 17\] \[\Rightarrow \] \[\omega '=17\,\,\omega \] So, value of\[x\]is\[17\].
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