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Q.

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-2m=10 kg

At the equator, the apparent weight is given by

mg'=mg-mω2R

Also, the angular speed of an equatorial point on the earth's surface is

ω=(2π/24×60×60)

  ω=7.27×10-5rad/s

Hence, now,    mg'=100-107.27×10-52×6.4×106

                               =  99.66N

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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]