Question

A wire elongates by 1.0 mm when a load W is hung from it. If this wire goes over a a pulley and two weights W each are hung at the two ends, he elongation of he wire will be 

पर्याय

•  0.5 m

• 1.0 mm

• 2.0 mm

• 4.0 mm

Answer 1

\[\text{ Let the Young's modulus of the material of the wire be Y } . \]

\[\text{  Force = Weight = W (given) }\]

\[\text{ Let C . S . A .  = A} \]

\[\text{ x = 1 mm = Elongation in the first case }\]

\[\text{ Length = L } \]

\[Y = \frac{\frac{W}{A}}{\frac{x}{L}} = \frac{WL}{Ax}\]

\[\text{Let y be the elongation on one side of the wire when put in a pulley }. \]

\[\text{ When put in a pulley, the length of the wire on each side }= \frac{L}{2}\]

\[ \frac{\frac{W}{A}}{\frac{y}{\frac{L}{2}}} = Y\]

\[ \Rightarrow \frac{\frac{W}{A}}{\frac{y}{\frac{L}{2}}} = \frac{WL}{\text{ Ax }}\]

\[ \Rightarrow y = \frac{x}{2}\]

\[\text{ Total elongation in the wire = 2y }= 2\left( \frac{x}{2} \right) = x = 1\text{ mm} \]