Three charges q- q and - 2 q are fixed on the vertices of an equilateral triangular plate of edge length a- This plate is in equilibrium between two very large plates having surface charge density -1 and -2 respectively- Find time period of small angular oscillation about an axis passing through its centroid and perpendicular to plane- Moment of inertia of the system about this axis is I-

The correct option is C 2π√(2ϵ_0I/√(3)qa|σ_1 σ_2|) Net dipole moment =√(3)qa τ = √(3)qa |σ_1 σ_2|θ/2ϵ_0=I α √(3)qa|σ_1 σ_2|/2ϵ_0=I (2π/T)^2 ⇒ T=2π√(2ϵ_0 I/√(3) ...

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

Byju's Answer

Standard XII

Physics

Other Examples of SHM

Three charges...

Question

Three charges q, q and - 2q are fixed on the vertices of an equilateral triangular plate of edge length a. This plate is in equilibrium between two very large plates having surface charge density $σ_{1}$ and $σ_{2}$ respectively. Find time period of small angular oscillation about an axis passing through its centroid and perpendicular to plane. Moment of inertia of the system about this axis is I.

$2 π \sqrt{\frac{ϵ_{0} I}{q a | σ_{1} - σ_{2} |}}$

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

$2 π \sqrt{\frac{ϵ_{0} I}{2 q a | σ_{1} - σ_{2} |}}$

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

$2 π \sqrt{\frac{2 ϵ_{0} I}{\sqrt{3} q a | σ_{1} - σ_{2} |}}$

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

$2 π \sqrt{\frac{2 ϵ_{0} I}{q a | σ_{1} - σ_{2} |}}$

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

Open in App

Solution

The correct option is C
$2 π \sqrt{\frac{2 ϵ_{0} I}{\sqrt{3} q a | σ_{1} - σ_{2} |}}$

Net dipole moment $= \sqrt{3} q a$

$τ = - \sqrt{3} q a \frac{| σ_{1} - σ_{2} | θ}{2 ϵ_{0}} = I α$

$\frac{\sqrt{3} q a | σ_{1} - σ_{2} |}{2 ϵ_{0}} = I {(\frac{2 π}{T})}^{2}$

$\Rightarrow T = 2 π \sqrt{\frac{2 ϵ_{0} I}{\sqrt{3} q a | σ_{1} - σ_{2} |}}$

Suggest Corrections

Similar questions

I

is moment of inertia of a uniform circular plate about an axis passing through any diameter of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through exact midpoint between centre and edge of the plate is:

Q. Two infinitely large sheets having charge densities

σ_{1}

and

σ_{2}

respectively

(σ_{1} > σ_{2})

are placed near each other separated by distance

d

.A charge

q

is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at an angle of

45^{o}

with the horizontal towards plate having charge density

σ_{2}

by distance

a

(a < d)

. Find work done by electric field in the process.

Q. I is moment of inertia of a thin square plate about an axis passing through opposite comers of plate. The moment of inertia of same plate about an axis perpendicular to the plane of plate and passing through its center is.

Q. A uniform triangular plate of mass

M

whose vertices are

A B C

has lengths

l, \frac{l}{\sqrt{2}}

and

\frac{l}{\sqrt{2}}

as shown in figure.. Find the moment of inertia of this plate about an axis passing through point

B

and perpendicular to the plane of the plate.

Q. A uniform triangular plate of mass

M

whose vertices are

A B C

has lengths

l, \frac{l}{\sqrt{2}}

and

\frac{l}{\sqrt{2}}

as shown in figure. Find the moment of inertia of this plate about an axis passing through point

B

and perpendicular to the plane of the plate.

Join BYJU'S Learning Program

The correct option is C 2π√2ϵ0I√3qa|σ1−σ2| Net dipole moment =√3qa τ=−√3qa|σ1−σ2|θ2ϵ0=Iα √3qa|σ1−σ2|2ϵ0=I(2πT)2 ⇒T=2π√2ϵ0I√3qa|σ1−σ2|