Two wires A and B are made of same material having ratio of lengths L_AL_B= 13 and their diameters ratio d_Ad_B=2. If both the wires are stretched using same force, what would be the ratio of their r…

Question

Two wires A and B are made of same material having ratio of lengths L_AL_B= 13 and their diameters ratio d_Ad_B=2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

Accepted Answer

Correct answer: B. (b) L_AL_R= 13 and d_Ad_R=2 L_A= F_AL_AA_AY_A and L_B= F_BL_BA_RY_R Given , F_A=F_B and Y_A=Y_B L_A L_B= F_AL_AA_AY_A F_BL_BA_BY_B= ( L_AL_B ) ( A_BA_A ) L_A L_B= ( L_AL_B ) ( 4d_B^2 4d_A^2 )= ( L_AL_B ) ( d_Bd_A )^2 L_A L_B= ( 13 ) ( 12 )^2= 112

$Two wires A and B are made of same material having ratio of lengths \frac{L _{A}}{L _{B}} = \frac{1}{3} and their diameters ratio \frac{d _{A}}{d _{B}} = 2 . If both the wires are stretched using same force, what would be the ratio of their respective elongations?$

Solution

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