Two wires of the same material (Young's modulus $Y$ ) and same length $L$ but radii $R$ and $2R$ 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

2R

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 2R respectively are joined end to

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

Quantrex Academy · Accepted Answer

Correct answer: C. 5w^ 2 L 8 πR ^ 2 Y

k _ 1 = (Y π(2R)2)/(L) , k _ 2 = (Y π(R)2)/(L) Equivalent (1)/(k1) + (1)/(k2) = L 4 YπR ^ 2 + (L)/(Y π R2) Since, k _ 1 x _ 1 = k _ 2 x _ 2 = w Elastic potential energy of the system U = (1)/(2) k _ 1 x _ 1 ^ 2 + (1)/(2) k _ 2 x _ 2 ^ 2 U = (1)/(2) k _ 1 ((w)/(k1)) 2 + (1)/(2) k _ 2 ((w)/(k2)) 2 =(1)/(2) w^ 2 (\ (1)/(k1) + (1)/(k2)\ = 1 2 w^ 2 ( 5L 4 YπR ^ 2 ) U = 5w^ 2 L 8 πYR ^ 2

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

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