Two rods A and B of the same length are made | vedclass

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(A) The resistance of a rod is given by $R = \rho \frac{l}{A}$.Since the volume $V = A \cdot l$,we can write $A = \frac{V}{l}$.Substituting this,$R =

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(A) The resistance of a rod is given by $R = \rho \frac{l}{A}$.Since the volume $V = A \cdot l$,we can write $A = \frac{V}{l}$.Substituting this,$R = \rho \frac{l^2}{V}$.Since density $\sigma = \frac{m}{V}$,we have $V = \frac{m}{\sigma}$.Thus,$R = \rho \frac{l^2 \sigma}{m}$.Given that the length $l$ and material (density $\sigma$ and resistivity $\rho$) are the same for both rods,we have $R \propto \frac{1}{m}$.Given $R_A : R_B = 1 : 2$,it follows that $m_A : m_B = 2 : 1$,which means $m_A > m_B$.The loss in weight when immersed in water is equal to the weight of the displaced water,which is $W_{loss} = V_{rod} \cdot \sigma_{water} \cdot g = \frac{m}{\sigma_{rod}} \cdot \sigma_{water} \cdot g$.Since $m_A > m_B$,the loss in weight in rod $A$ will be more than in rod $B$.

Two rods $A$ and $B$ of the same length are made of the same material. The ratio of their resistances is $1 : 2$. If the rods are immersed in water,the loss in their weight will be:

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