An object is weighed at the North pole by a beam balance and a spring balance, giving readings of $W_{B}$ and $W_{S}$ respectively. It is again weighed in the same manner at the equator, giving readings of $W_{B}^{'}$ and $W_{S}^{'}$ respectively. Assume that the acceleration due to gravity is the same everywhere and that the balances are quite sensitive.

W_{B} = W_{S}

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W_{B}^{'} = W_{S}^{'}

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W_{B} = W_{B}^{'}

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W_{S}^{'} = W_{S}

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Solution

The correct options are
A $W_{B} = W_{S}$
B $W_{B} = W_{B}^{'}$
Beam balance gives the weight irrespective of the rotational effect of the earth, whereas in spring balance, $ω$ also accounts.
At the poles rotational effect is zero, but at equator it is maximum
Therefore, $W_{B} = {W^{1}}_{B} = W_{S}$
and, ${W^{1}}_{S}$ is lesser than all the above.

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The correct options are A WB=WS B WB=W′BBeam balance gives the weight irrespective of the rotational effect of the earth, whereas in spring balance, ω also accounts.At the poles rotational effect is zero, but at equator it is maximumTherefore, WB=W1B=WSand, W1S is lesser than all the above.