Question

Line $PQ$ is parallel to $y$ -axis and moment of inertia of a rigid body about $PQ$ line is given by $I=2x^{2}-12x+27,$ where $x$ is in meter and $I$ is in $\text{k}\text{g}$ $\text{m}^{2}$ . The minimum value of $I$ is:

• A. $27 \, \text{k}\text{g} \, \text{m}^{2}$
• B. $11 \, \text{k}\text{g} \, \text{m}^{2}$
• C. $17 \, \text{k}\text{g} \, \text{m}^{2}$
• D. $9 \, \text{k}\text{g} \, \text{m}^{2}$

Answer 1

Answer: (D)

$I=2x^{2}-12x+27$
$\frac{d I}{d x} \, =4x-12$
For minimum or maximum
$\frac{d I}{d x} \, =0\Rightarrow x=3$
$\frac{d^{2} I}{d x^{2}}=4.$ Hence $I$ is minimum at $x=3$
$\text{I}=9 \, \text{k}\text{g} \, \text{m}^{2}$