A metre scale is balanced on a knife edge at | vedclass

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(B) Let the mass of the metre scale be $m$. The centre of mass of the uniform metre scale is at the $50.0\, cm$ mark.When the scale is balanced at the

Vedclass · Accepted Answer

$6$

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(B) Let the mass of the metre scale be $m$. The centre of mass of the uniform metre scale is at the $50.0\, cm$ mark.When the scale is balanced at the $40.0\, cm$ mark,the torque due to the coins must balance the torque due to the weight of the scale.The mass of the two coins is $2 	imes 10\, g = 20\, g = 0.02\, kg$.The distance of the coins from the knife edge is $|40.0\, cm - 10.0\, cm| = 30.0\, cm = 0.3\, m$.The distance of the centre of mass of the scale from the knife edge is $|50.0\, cm - 40.0\, cm| = 10.0\, cm = 0.1\, m$.Applying the principle of moments (balancing torques about the knife edge):$(0.02\, kg) 	imes g 	imes (0.3\, m) = m 	imes g 	imes (0.1\, m)$$0.006 = 0.1m$$m = 0.06\, kg = 6 	imes 10^{-2}\, kg$.Comparing this with $x 	imes 10^{-2}\, kg$,we get $x = 6$.

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