List-I List-II (a) MI of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The moment of inertia $(MI)$ of a rod of mass $M$ and length $L$ is given by:$1$. About an axis passing through the center and perpendicular to th

Vedclass · Accepted Answer

$(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)$

Vedclass · Answer

(A) The moment of inertia $(MI)$ of a rod of mass $M$ and length $L$ is given by:$1$. About an axis passing through the center and perpendicular to the rod: $I = \frac{ML^2}{12}$.$2$. About an axis passing through one end and perpendicular to the rod: $I = \frac{ML^2}{3}$.Applying these formulas:$(a)$ For mass $M$,length $L$,axis through midpoint: $I = \frac{ML^2}{12}$ (Matches $iii$).$(b)$ For mass $2M$,length $L$,axis through end: $I = \frac{(2M)L^2}{3} = \frac{2ML^2}{3}$ (Matches $iv$).$(c)$ For mass $M$,length $2L$,axis through midpoint: $I = \frac{M(2L)^2}{12} = \frac{4ML^2}{12} = \frac{ML^2}{3}$ (Matches $ii$).$(d)$ For mass $2M$,length $2L$,axis through end: $I = \frac{(2M)(2L)^2}{3} = \frac{2M(4L^2)}{3} = \frac{8ML^2}{3}$ (Matches $i$).Thus,the correct matching is $(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)$.

List-$I$	List-$II$
$(a)$ $MI$ of the rod (length $L$,mass $M$,about an axis $\perp$ to the rod passing through the midpoint)	$(i) \frac{8ML^2}{3}$
$(b)$ $MI$ of the rod (length $L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends)	$(ii) \frac{ML^2}{3}$
$(c)$ $MI$ of the rod (length $2L$,mass $M$,about an axis $\perp$ to the rod passing through its midpoint)	$(iii) \frac{ML^2}{12}$
$(d)$ $MI$ of the rod (length $2L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends)	$(iv) \frac{2ML^2}{3}$

Similar Questions

Find the moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane.

From a circular disc of radius $R$ and mass $9M$,a small disc of mass $M$ and radius $R/3$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

On account of the melting of ice at the North Pole,the moment of inertia of the spinning Earth:

$A$ metallic solid sphere is rotating about its diameter as an axis of rotation. If the temperature is increased by $200^{\circ} C$, the percentage increase in its moment of inertia is (Coefficient of linear expansion of the metal $= 10^{-5} /^{\circ} C$) (in $\%$)

Can the moment of inertia of the same body be different?

Vedclass Test Series

Exam Paper Generator

Online Exam Module