Two identical thin rods of mass M kg and len | vedclass

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

Question

(B) Let the vertical rod be $1$ and the horizontal rod be $2$.For rod $1$, the moment of inertia about an axis passing through $P$ (its end) and perpe

Vedclass · Accepted Answer

$17$

Vedclass · Answer

(B) Let the vertical rod be $1$ and the horizontal rod be $2$.For rod $1$, the moment of inertia about an axis passing through $P$ (its end) and perpendicular to its length is $I_1 = \frac{ML^2}{3}$.For rod $2$, the moment of inertia about its center of mass is $I_{cm} = \frac{ML^2}{12}$. Using the parallel axis theorem, the moment of inertia about an axis passing through $P$ and perpendicular to the plane is $I_2 = I_{cm} + Md^2$, where $d = L$ is the distance from $P$ to the center of rod $2$.$I_2 = \frac{ML^2}{12} + M(L)^2 = \frac{13ML^2}{12}$.The total moment of inertia is $I = I_1 + I_2 = \frac{ML^2}{3} + \frac{13ML^2}{12} = \frac{4ML^2 + 13ML^2}{12} = \frac{17ML^2}{12}$.Comparing this with $\frac{x}{12} ML^2$, we get $x = 17$.

Two identical thin rods of mass $M \ kg$ and length $L \ m$ are connected as shown in the figure. The moment of inertia of the combined rod system about an axis passing through point $P$ and perpendicular to the plane of the rods is $\frac{x}{12} M L^2 \ kg \ m^2$. The value of $x$ is . . . . . . .

Similar Questions

$A$ thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma (r) = kr^2$,where $r$ is the distance from its centre. Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is

The moment of inertia of an object is effective during:

How does the moment of inertia depend on the angular momentum?

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

$A$ wire of mass $M$ is bent into a circular shape of radius $R$. What is the moment of inertia about its diameter?

Vedclass Test Series

Exam Paper Generator

Online Exam Module