Question

A tapered circular rod of diameter varying from $20mm$ to $10mm$ is connected to another uniform circular rod of diameter $10mm$ as shown in the following figure. Both bars are made of same material with the modulus of elasticity, $E=2\times {10}^5$MPa. When subjected to a load $P=30\pi kN$, the deflection at point $A$ is

• A. 15

Answer 1

The correct option is A 15

Total elongation,
$\Delta ={\Delta }_{AB}+{\Delta }_{BC}$
$=\frac{30\pi \times 1.5}{\frac{\pi \times (0.01{)}^2}{4}\times 2\times {10}^5}+\frac{30\pi \times 2}{\frac{\pi \times \left(0.01\right)\times \left(0.02\right)}{4}\times 2\times {10}^5}$
$=\frac{30\times 1.5\times 4}{(0.01{)}^2\times 2\times {10}^5}+\frac{30\times 2\times 4}{0.01\times 0.02\times 2\times {10}^5}$
$=9+6=15mm$