question_answer

A box weighs 196 N on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take \[g=10\text{ }m{{s}^{2}}\]at the north pole and the radius of the earth = 6400 km)  [JEE MAIN Held on 07-01-2020 Evening]

A)  194.66 N                     

B)  195.66 N

C)  195.32 N         

D)       194.32 N Correct Answer: C Solution : [c] Weight at equator = \[m{{g}^{'}}\]

\[=m\,(g\text{ }{{\omega }^{2}}R)\]

\[mg=196\text{ }N\text{ }\Rightarrow \text{ }m=19.6\text{ }kg\]

\[\Rightarrow \,\,mg'=19.6\left[ 10-{{\left( \frac{2\pi }{24\times 3600} \right)}^{2}}\times 6400\times {{10}^{3}} \right]\,N\]

= 19.6[10 – 0.034] = 195.33 N