Two wires of the same material (Young's modulus $=Y$ ) and same length $L$ but radii $R$ and $2 R$ respectively, are joined end to end and a weight $w$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is

Question

Two wires of the same material (Young's modulus

=Y

) and same length

L

but radii

R

and

2 R

respectively, are joined end to end and a weight

w

is suspended from the combination as shown in the figure. The elastic potential energy in the system is Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2 R respectively, are joined end

Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2 R respectively, are joined end

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Correct answer: C. (5 w^2 L)/(8 π R^2 Y)

aligned & Δ l_1=(w L)/((4 π R^2) Y), Δ l_2=(w L)/(π R^2 Y) & U=(1)/(2) K_1(Δ l_1)^2+(1)/(2) K_2(Δ l_2)^2 &=(1)/(2) × (Y(4 π R^2))/(L) ×[(w L)/(4 π R^2 Y)]^2+(1)/(2) × (Y(π R^2))/(L) & ×[(w L)/(π R^2 Y)]^2( K=(Y A)/(L)) &=(5 w^2 L)/(8 π R^2 Y) aligned

Two wires of the same material (Young's modulus =Y ) and same...

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