The reading of a spring balance corresponds to 100 N while situated at the north pole and a body is kept on it. The weight record on the same scale, if it is shifted to the equator, is (Take, g = 10 ms-2 and radius of the earth, R = 6.4 X 106m) [AIIMS 2015]
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a
99.66 N
b
110 N
c
97.66 N
d
106 N
answer is A.
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Detailed Solution
At the pole, the weight is same as the actual weight.Thus, 100 N=m10 ms-2⇒m=10 kgAt the equator, the apparent weight is given bymg'=mg-mω2RAlso, the angular speed of an equatorial point on the earth's surface isω=(2π/24×60×60)⇒ ω=7.27×10-5rad/sHence, now, mg'=100-107.27×10-52×6.4×106 = 99.66N