Moment of inertia of a uniform rod of length L and mass M, about an axis passing through L/4 from one end and perpendicular to its length is

Question

Moment of inertia of a uniform rod of length L and mass M, about an axis passing through L/4 from one end and perpendicular to its length is (A) (7/36)ML2 (B) (7/48)ML2 (C) (11/48)ML2 (D) (ML2/12)

Tardigrade Admin · Accepted Answer

Moment of inertia of a uniform rod of length

L

and mass

M

about an axis passing through the centre and perpendicular to its length is given by

I_{0} = \frac{M L ^{2}}{12}

..(i)
According to the theorem of parallel axes, moment of inertia of a uniform rod of length

L

and mass

M

about an axis passing through

L /4

from one end and perpendicular to its length is given by

I = I_{0} + M (\frac{L}{4})^{2} = \frac{M L ^{2}}{12} + \frac{M L ^{2}}{16} = \frac{7 M L ^{2}}{48}

(Using (i))

Q. Moment of inertia of a uniform rod of length $L$ and mass $M$ , about an axis passing through $L /4$ from one end and perpendicular to its length is

$\frac{7}{36} M L^{2}$

$\frac{7}{48} M L^{2}$

$\frac{11}{48} M L^{2}$

$\frac{M L ^{2}}{12}$

Q. Moment of inertia of a uniform rod of length L and mass M, about an axis passing through L/4 from one end and perpendicular to its length is

367​ML2

487​ML2

4811​ML2

12ML2​

Q. Moment of inertia of a uniform rod of length $L$ and mass $M$ , about an axis passing through $L /4$ from one end and perpendicular to its length is

$\frac{7}{36} M L^{2}$

$\frac{7}{48} M L^{2}$

$\frac{11}{48} M L^{2}$

$\frac{M L ^{2}}{12}$