Question

A solid cylindrical rod of radius $3mm$ gets depressed under the influence of a load through $8mm$. The depression produced in an identical hollow rod with outer and inner radii of $4mm$ and $2mm$ respectively, will be

• A. 2.7mm
• B. 1.9mm
• C. 3.2mm
• D. 7.7mm

Answer 1

The correct option is A 2.7mm

Depression in Solid cylinder ${\delta }_1=8mm$
Its radius $r_1=3mm$
Outer radius of Hollow cylinder $R_2=4mm$
Inner radius of Hollow cylinder $r_2=2mm$
Let depression in this cylinder be ${\delta }_2$.
Depression $\delta =\frac{W{l}^3}{12\pi r^{4}Y}$
From the above equation we know that $\delta$ is proportional to $\frac{1}{r^4}$
Hence, we have
$\frac{{\delta }_1}{{\delta }_2}=\frac{{R_2}^4-{r_2}^4}{r_1^4}$
Substituting the values in above equation, we get
${\delta }_2=2.7mm$