Physics

Moment of Inertia

39 Questions

The moment of inertia measures the resistance of a rigid body to changes in its rotational motion. Questions cover calculating inertia for uniform cylinders, solid spheres, and thin spherical shells. This core physics topic is vital for engineering aspirants and civil services preliminary tests.

Uniform cylinder inertiaSolid sphere inertiaAngular momentum equationRigid body rotationPoint mass inertia

Moment of Inertia Questions

Multiple choice general knowledge science & technology

Inertia of ..... types?

  1. 2

  2. 3

  3. 8

  4. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Inertia has three types: (1) Inertia of rest - tendency to remain at rest, (2) Inertia of motion - tendency to remain in motion, and (3) Inertia of direction - tendency to maintain direction of motion. These are all manifestations of Newton's First Law of Motion (Law of Inertia).

Multiple choice physics forces - vectors and moments the turning of couple couple rotational motion of a rigid body and moment of inertia turning effect of force

Which of the following is/are the properties of moment of a couple?

  1. It tends to produce pure rotation.

  2. It is different about any point in the plane of lines of action of the forces.

  3. It can be replaced by any other couple of the same moment.

  4. The resultant of set of two or more couples is equal to the sum of the moments of the individual couples.
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
Explanation

A couple when applied to a body it produce 

(i) Pure rotation
(ii) It can be replaced by any other couple of same moment.
(iii) The resultant of set of two or more couples is equal to the sum of moment of individuals couples.

Multiple choice physics turning on a pivot the turning effect of a force moment of force or torque turning effect of force couple

Name the factor on which moment of inertia of a body depends .

  1. Mass

  2. Force

  3. Distance from rotating axis.

  4. Density
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Moment of inertia of a body depends  on the body's mass distribution and the axis of rotation.
The moment of inertia of a body is directly proportional to its mass and increases as the mass is moved further from the axis of rotation.
Answer (A) Mass & (C) Distance from rotating axis.

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

A body having its centre of mass at the origin has three of its particles at $(a,0,0),(0,a,0),(0,0,a)$ the moment of inertia of the body about X and Y axis are $0.2kg{m _2}$ the moment of inertia about its Z axis is 

  1. is $0.20kg{m _2}$
  2. is $0.40kg{m _2}$
  3. $0.20\sqrt 2 kg{m^2}$

  4. cannot be deducted with this information
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The moment of inertia depends on the distribution of mass relative to the axis. With only three particles at (a,0,0), (0,a,0), and (0,0,a), the mass distribution is not symmetric enough to determine the Z-axis moment of inertia solely from the X and Y values without knowing the masses or the full body configuration.

Multiple choice physics turning effects of forces stability and centre of mass center of mass centre of mass

Find the coordination of center of mass of a uniform semicircle closed wire frame with respect to the origin which is at its center.The radius of the circular portion is R.                

  1. $\left( {\dfrac{{4R}}{{3\pi }},0} \right)$
  2. $\left( {\dfrac{{2R}}{{\pi }},0} \right)$
  3. $\left( {\dfrac{R}{{\pi + 2}},0} \right)$
  4. $\left( {\dfrac{2R}{{\pi + 2}},0} \right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that, $x+cm=\cfrac{4}{\pi R^2}\int^0 _R{-t^2 dt}$

$=\cfrac{4}{\pi R^2}|-\cfrac{t^3}{R}|^0 _R=\cfrac{4}{\pi R^2}(\cfrac{R^3}{3})=\cfrac{4R}{3\pi}$
Thus, co-ordinates should be $=[\cfrac{4}{3\pi},0]$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole of dipole moment $p$ is placed in a uniform electric field $E$ in stable equilibrium position. Its moment of inertia about the centroidal axis is $I$. If it is displaced slightly from its mean position find the period of small oscillations.

  1. $2\pi \sqrt{\dfrac{I}{2pE}}$
  2. $2\pi \sqrt{\dfrac{2I}{pE}}$
  3. $2\pi \sqrt{\dfrac{I}{pE}}$
  4. $\pi \sqrt{\dfrac{2I}{pE}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Dipole moment $=p$
electric field $=E$
centroid axis $=I$
Explanation
When displaced at an angle $\theta $ from its mean position the magnitude of restoring torque is $T=-psin\theta $
For small angular displacement $\sin\theta \approx \theta $
$T=-pE\theta $
$\alpha =\dfrac { T }{ I } =-\left( \dfrac { PE }{ I }  \right) \theta $
    $={ -w }^{ 2 }\theta $
${ w }^{ 2 }=\dfrac { PE }{ I } $
$T=2\pi \sqrt { \dfrac { I }{ PE }  } $
($P.E=$ moment in electric field)
Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

Density of solid sphere is varied by $\rho = \rho _0 \lgroup 1 + \frac{r}{R} \rgroup$ where $0 \leq r \leq R$, R is the radius of the sphere. Moment of inertia of sphere w.r.t. axis passing through its centre will be : ($\rho _0$ is constant)

  1. $\dfrac{44}{45} \pi \rho _0 R^5$
  2. $\dfrac{44}{45} \pi \rho _0 R^4$
  3. $\dfrac{44}{35} \pi \rho _0 R^5$
  4. $\dfrac{48}{45} \pi \rho _0 R^5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} dM=s\left( { 4\pi { x^{ 2 } }dx } \right)  \ ={ \rho _{ 0 } }\left( { 1+\dfrac { x }{ R }  } \right) \left( { 4\pi { x^{ 2 } }dx } \right)  \ dI=\dfrac { 2 }{ 3 } dM{ x^{ 2 } } \ \dfrac { 2 }{ 3 } { \rho _{ o } }\int _{ 0 }^{ R }{ \left( { 4\pi { x^{ 4 } }dx+\dfrac { { 4\pi  } }{ R } { x^{ 5 } }dx } \right)  }  \ =\dfrac { { 8\pi { \rho _{ 0 } } } }{ 3 } \left[ { \dfrac { { { x^{ 5 } } } }{ 5 } +\dfrac { { { R^{ 5 } } } }{ 6 }  } \right]  \ =\dfrac { 8 }{ 3 } \pi { \rho _{ o } }\times \dfrac { { 11{ R^{ 5 } } } }{ { 30 } }  \ =\dfrac { { 44 } }{ { 45 } } \pi { \rho _{ 0 } }{ R^{ 5 } } \end{array}$

Hence,
option $(A)$ is correct answer.

Multiple choice

The moment of inertia of a rigid body is a measure of its:

  1. Mass

  2. Density

  3. Resistance to rotation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The moment of inertia of a rigid body is a measure of its resistance to rotation. It is defined as the sum of the products of the masses of the particles of the body and the squares of their distances from the axis of rotation. A larger moment of inertia indicates a greater resistance to rotation.

Multiple choice

What is the significance of the moment of inertia in Attitude Dynamics?

  1. It determines the spacecraft's resistance to changes in angular velocity

  2. It affects the spacecraft's stability and controllability

  3. It influences the spacecraft's orbital period

  4. It governs the spacecraft's attitude maneuverability
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Moment of inertia plays a crucial role in determining the spacecraft's resistance to changes in angular velocity, which is essential for attitude control.

Multiple choice

What is the name of the method developed by Bhaskara I for finding the moment of inertia of a region?

  1. Bhaskara's Method

  2. Moment of Inertia Method

  3. Parallel Axis Theorem

  4. Perpendicular Axis Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara's Method is a method for finding the moment of inertia of a region developed by Bhaskara I in the 7th century. It is based on the idea of dividing the region into an infinite number of small pieces and then summing their masses and distances from a given axis.