A box weighs <math> <mn>196</mn> <mtext> </mtext> <mi mathvariant="normal">N</mi> </math> 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 <math> <mi mathvariant="normal">g</mi> <mo>=</mo> <mn>10</mn> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> at the north pole and the radius of the earth <math> <mo>=</mo> <mn>6400</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">m</mi> </math> )

W equator = W pole - m ω 2 R = 196 - 19.6 × 2 π 24 × 60 × 60 2 × 6400 × 10 3 = 195.33 N

A box weighs <math> <mn>196</mn> <mtext> </mtext> <mi mathvariant="normal">N</mi> </math> 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 <math> <mi mathvariant="normal">g</mi> <mo>=</mo> <mn>10</mn> <msup> <mrow> <mrow> <mtext> </mtext> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> at the north pole and the radius of the earth <math> <mo>=</mo> <mn>6400</mn> <mtext> </mtext> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">m</mi> </math> &nbsp;) &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

Ask & Answer Question

Option 1 -

$194.66 N$

Option 2 -

$194.32 N$

Option 3 -

$195.32 N$

Option 4 -

$195.66 N$

2 Views | Posted 3 months ago

Answered by

alok kumar singh | Contributor-Level 10

3 months ago

Correct Option - 3

Detailed Solution:

$W_{equator} = W_{pole} - m ω^{2} R$

$\begin{array}{r} = 196 - 19.6 \times {(\frac{2 π}{24 \times 60 \times 60})}^{2} \times 6400 \times 10^{3} \\ = 195.33 N \end{array}$