A tapered circualr rod of diameter varying from $30 m m$ to $15 m m$ is connected to another circular rod of diameter $15 m m$ as shown in figure. Both bars are of same material with the modulus of elasticity $E = 2 \times 10^{5} N / m m^{2}$ and subjected to axial load of $100 k N$ , then deflection of a bar at the free end is ____ $m m$

9.9

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Solution

The correct option is A 9.9
Deflection at free end $C$

$= Δ_{A B} + Δ_{B C}$

$= \frac{4 P_{1} l_{1}}{π E (D_{1} D_{2})} + \frac{4 P_{2} l_{2}}{π D_{2}^{2} E}$

Here, $P_{1} = P_{2} = 100 k N$

$l_{1} = 3 m, l_{2} = 2 m$

$E = 2 \times 10^{5} N / m m^{2}$

$D_{1} = 30 m m$

$D_{2} = 15 m m$

$Δ_{C} = \frac{4 \times 100 \times 10^{3} \times 3 \times 10^{3}}{π \times 2 \times 10^{5} (30 \times 15)} + \frac{4 \times 100 \times 10^{3} \times 2 \times 10^{3}}{π \times 15^{2} \times 2 \times 10^{5}} = 9.9 m m$

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