
The moment of inertia of a body rotating about a given axis is $12kg m^2$ in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is $5cm$ and the unit of mass is $10g$?
A) $2.4 \times 10^3$
B) $6.0 \times 10^3$
C) $5.4 \times 10^3$
D) $4.8 \times 10^5$
Answer
133.8k+ views
Hint: The moment of inertia of an object is a numerical value that can be calculated for any rigid body that is undergoing a physical rotation around a fixed axis. It is based not only on the physical size of the object and the distribution of its mass, but also on the specific configuration of how the object is moving.
Complete step by step solution:
\(Given,I = 12kg{m^2}\\{\rm{\text{For new system}}}\\ \Rightarrow {\rm{unit length = 5cm}}\\{\rm{unit mass = 10gm}}\\ \Rightarrow {\rm{I = 12}} \times {\rm{1000}} \times {\rm{1}}{{\rm{0}}^4}gc{m^2}\\ \Rightarrow I = 12 \times \dfrac{{1000 \times {{10}^3}}}{{25 \times 10}} \times 10g \times 5c{m^2}\\ \Rightarrow I = 48000 \times 10g \times 5c{m^2}\\\therefore I = 4.8 \times {10^5}\)
Additional Information:
Any moving object has kinetic energy. We know how this is translated for a body undergoing conversion, but how about a rigid body undergoing rotation? This may sound complicated because each point of a rigid body has a different velocity. However, we can use angular velocity - which is the same for the entire rigid body - to express the kinetic energy for a rotating object.
Rotational inertia plays a role similar to mass in linear mechanics in rotational mechanics. Actually, the rotational inertia of an object depends on its mass. It also depends on the distribution of that mass relative to the axis of rotation.
It becomes more difficult to change the rotational velocity of a system when a mass moves past the axis of rotation. Intuitively, this is because the mass is now moving around the circle with greater speed (due to higher speed) and because the momentum vector is changing more rapidly. Both these effects depend on the distance from the axis.
Rotational inertia is given the symbol III. For a single body such as the tennis ball of mass m, rotating at radius r from the axis of rotation the rotational inertia is $I$ = $mr^2$.
Note: The parallel axis theorem allows us to find the moment of inertia of an object about a point o as long as we know the moment of inertia of the shape around its centroid c, mass m and distance d between points o and c.
$Io=Ic + md^2$
Moment of Inertia is the inherent property of matter in rotating motion, the moment of inertia of a body is a measure of its inertia. The greater the moment of inertia, the greater the torque required to create the given angular acceleration.
Complete step by step solution:
\(Given,I = 12kg{m^2}\\{\rm{\text{For new system}}}\\ \Rightarrow {\rm{unit length = 5cm}}\\{\rm{unit mass = 10gm}}\\ \Rightarrow {\rm{I = 12}} \times {\rm{1000}} \times {\rm{1}}{{\rm{0}}^4}gc{m^2}\\ \Rightarrow I = 12 \times \dfrac{{1000 \times {{10}^3}}}{{25 \times 10}} \times 10g \times 5c{m^2}\\ \Rightarrow I = 48000 \times 10g \times 5c{m^2}\\\therefore I = 4.8 \times {10^5}\)
Additional Information:
Any moving object has kinetic energy. We know how this is translated for a body undergoing conversion, but how about a rigid body undergoing rotation? This may sound complicated because each point of a rigid body has a different velocity. However, we can use angular velocity - which is the same for the entire rigid body - to express the kinetic energy for a rotating object.
Rotational inertia plays a role similar to mass in linear mechanics in rotational mechanics. Actually, the rotational inertia of an object depends on its mass. It also depends on the distribution of that mass relative to the axis of rotation.
It becomes more difficult to change the rotational velocity of a system when a mass moves past the axis of rotation. Intuitively, this is because the mass is now moving around the circle with greater speed (due to higher speed) and because the momentum vector is changing more rapidly. Both these effects depend on the distance from the axis.
Rotational inertia is given the symbol III. For a single body such as the tennis ball of mass m, rotating at radius r from the axis of rotation the rotational inertia is $I$ = $mr^2$.
Note: The parallel axis theorem allows us to find the moment of inertia of an object about a point o as long as we know the moment of inertia of the shape around its centroid c, mass m and distance d between points o and c.
$Io=Ic + md^2$
Moment of Inertia is the inherent property of matter in rotating motion, the moment of inertia of a body is a measure of its inertia. The greater the moment of inertia, the greater the torque required to create the given angular acceleration.
Recently Updated Pages
JEE Main 2025 Session 2 Form Correction (Closed) – What Can Be Edited

Sign up for JEE Main 2025 Live Classes - Vedantu

JEE Main Books 2023-24: Best JEE Main Books for Physics, Chemistry and Maths

JEE Main 2023 April 13 Shift 1 Question Paper with Answer Key

JEE Main 2023 April 11 Shift 2 Question Paper with Answer Key

JEE Main 2023 April 10 Shift 2 Question Paper with Answer Key

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Class 11 JEE Main Physics Mock Test 2025

JEE Main Chemistry Question Paper with Answer Keys and Solutions

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Motion In A Plane: Line Class 11 Notes: CBSE Physics Chapter 3
