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. 5 w ^ 2 L 8 π R ^ 2 Y

k _ 1 = Y π (2R) ^ 2 L , k _ 2 = Y π (R) ^ 2 L Equivalent 1 k _ 1 + 1 k _ 2 = L 4 Y π R ^ 2 + L Y π R ^ 2 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 k _ 1 ) ^ 2 + (1)/(2) k _ 2 ( w k _ 2 ) ^ 2 = (1)/(2) w ^ 2 \ 1 k _ 1 + 1 k _ 2 \ = (1)/(2) w ^ 2 ( 5L 4 Y π R ^ 2 ) U = 5 w ^ 2 L 8 π YR ^ 2

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

Options

Correct answer

Step-by-step solution

More from Mechanical Properties of Solids