MEDIUMNEET College Predictor
ApplyKnow possible Govt/Private MBBS/BDS Colleges based on your NEET rank
Moment Of Inertia Of A Rod MCQ - Practice Questions with Answers
Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET
Quick Facts
-
Moment of inertia of a Rod is considered one of the most asked concept.
-
10 Questions around this concept.
Solve by difficulty
The moment of inertia of a uniform cylinder of length and radius
about its perpendicular bisector is
. What is the ratio
such that the moment of inertia is minimum?
Three identical rods, each of length l are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is
Four identical thin rods each of mass $M$ and length $\ell$, form a square frame. The moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is :
There is a rod of length L and mass M; one line is passing through the centre of the rod and another line is passing through the end of the rod; The radius of gyrations ratio of this rod for the given cases (concerning the line positions) centre/end is
A thin rod of length is suspended from a point from on its length which is at a distance
from its centre, for what value of
time period of oscillation will be minimum -
A tube of length 1m is filled completely with an incompressible liquid with of mass 1kg and closed at both ends. The tube is rotated in a horizontal plane about one of its ends with a uniform angular velocity of 2rad/s. The force exerted by the liquid ath the other end is
Concepts Covered - 1
Moment of inertia of a Rod
Let I=Moment of inertia of a ROD about an axis through its center and perpendicular to it
To calculate I (Moment of inertia of rod)
Consider a uniform straight rod of length L, mass M and having center C
mass per unit length of the rod = $\lambda=\frac{M}{L}$
Take a small element of mass dm with length dx at a distance x from point C.
$$
\begin{aligned}
d m & =\lambda \cdot d x=\frac{M}{L} \cdot d x \\
\Rightarrow d I & =x^2 d m
\end{aligned}
$$
Now integrate this dl between the limits $x=-\frac{L}{2}$ to $\frac{L}{2}$
$$
I=\int d I=\int x^2 d m=\int_{\frac{-L}{2}}^{\frac{L}{2}} \frac{M}{L} x^2 * d x=\frac{M}{L} \int_{\frac{-L}{2}}^{\frac{L}{2}} x^2 d x=\frac{M L^2}{12}
$$
Study it with Videos
Moment of inertia of a Rod"Stay in the loop. Receive exam news, study resources, and expert advice!"
Get Answer to all your questions
NEET Articles
Back to top