You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Radius of Gyration

A rod PQ of m...

Question

A rod PQ of mass 'm' and length 'l' rotated about and axis through 'p' as shown in figure.Find the moment of inertia about axis of Rotation

\frac{3 g}{2 L}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{m l^{2}}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{m l^{2}}{3} {cos}^{2} θ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{m l^{2}}{3} + m l^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{3 g}{2 L}$
$\begin{matrix} T o r q u e o n t h e r o d = m o m e n t o f w e i g h t o f t h e r o d a b o u t P T = m g \frac{L}{2} - - - (1) M o m e n t o f i n e r t i a o f r o d a b o u t, p = \frac{M L^{2}}{3} - - - (2) F r o m e q u a t i o n (1) a n d (2), w e g e t M g \frac{L}{2} = \frac{M L^{2}}{3} α ∴ α = \frac{3 g}{2 L} \end{matrix}$
Hence, option $A$ is the correct answer.

Suggest Corrections

Similar questions

Q. A uniform rod of mass

m

and length

L

is rotated about an axis passing through the point

P

as shown in figure. The magnitude of angular momentum of the rod, about the rotational axis

y y^{'}

passing through the point

P

A thin rod of mass M and length L is rotating about an axis perpendicular to length of rod and passing through its centre. If half of the total rod that lies at one side of axis is cut and removed then the moment of inertia of remaining rod is

Q. A rod of length

L

rotates about an axis passing through one of its ends and perpendicular to its plane. If the linear mass density of the rod varies as

ρ = (A r^{3} + B) k g / m

, then the moment of inertia of the rod about the given axis of rotation is

Q. Two objects of same mass

m

are attached at end of a light rod of length

l

and rotating about axis

O O^{'}

as shown in the figure. The moment inertia of the system about the axis

O O^{'}

Q. A rod of length

l = 10 π m

is rotating about a perpendicular bisector passing through its C.O.M and having moment of inertia,

π^{2} {kg-m}^{2}

. If same rod is bent into semi circular arc of radius

r

as shown in figure and rotated about the same axis in same plane, then moment of inertia of arc will be

Join BYJU'S Learning Program

A rod PQ of mass 'm' and length 'l' rotated about and axis through 'p' as shown in figure.Find the moment of inertia about axis of Rotation

The correct option is A 3g2LTorqueontherod=momentofweightoftherodaboutPT=mgL2−−−(1)Momentofinertiaofrodabout,p=ML23−−−(2)Fromequation(1)and(2),wegetMgL2=ML23α∴α=3g2LHence, option A is the correct answer.