First slide

Elastic behaviour of solids

Question

Wires A and B are connected with blocks P and Q, as shown. The ratio of lengths, radii and Young's modulus of wires A and B are r, 2r and 3r respectively (r is a constant). Find the mass of block P it ratio of increase in their corresponding lengths is $\frac{1}{6 r^{2}}$ . The mass of the block Q is 3M.

Moderate

A

M
B

3M
C

6M
D

9M

Solution

$\begin{array}{l} Δl = \frac{FL}{AY} \\ \begin{matrix} \frac{(Δl)_{A}}{(Δl)_{B}} = (\frac{F_{A}}{F_{B}}) (\frac{L_{A}}{L_{B}}) (\frac{A_{B}}{A_{A}}) (\frac{Y_{B}}{Y_{A}}) \end{matrix} \\ = (\frac{KM}{3 M}) (r) {(\frac{1}{2 r})}^{2} (\frac{1}{3 r}) = \frac{K}{36 r^{2}} = \frac{1}{6 r^{2}} (given) \\ K = 6 \end{array}$
Mass of block P = 6M

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