Line PQ is parallel to y -axis and moment of inertia of a rigid body about PQ line is given by I=2x2-12x+27, where x is in meter and I is in textk textg textm2 . The minimum value of I is:

Question

Line PQ is parallel to y -axis and moment of inertia of a rigid body about PQ line is given by I=2x2-12x+27, where x is in meter and I is in textk textg textm2 . The minimum value of I is: <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/58d1931d93ed35c6e143b4bb9aad7800-.png" /> (A) 27 textk textg textm2 (B) 11 textk textg textm2 (C) 17 textk textg textm2 (D) 9 textk textg textm2

Tardigrade Admin · Accepted Answer

I=2x2-12x+27 (d I/d x) =4x-12 For minimum or maximum (d I/d x) =0⇒ x=3 (d2 I/d x2)=4. Hence I is minimum at x=3 textI=9 textk textg textm2

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

$27 k g m^{2}$

$11 k g m^{2}$

$17 k g m^{2}$

$9 k g m^{2}$

$I = 2 x^{2} - 12 x + 27$
$\frac{d I}{d x} = 4 x - 12$
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 $x = 3$
$I = 9 k g m^{2}$

Q. Line PQ is parallel to y -axis and moment of inertia of a rigid body about PQ line is given by I=2x2−12x+27, where x is in meter and I is in kg m2 . The minimum value of I is:

27kgm2

11kgm2

17kgm2

9kgm2