The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be_________m. Given the length of the rod is \(10\sqrt3\; m\).
Correct Answer: 5
Solution and Explanation
\(I = \frac{ML^2}{12}\)
= \(MK^2\)
\(K = \frac{L}{ \sqrt{12}}\)
= \(\frac{10\sqrt{3}}{\sqrt{12}}\)
= \(5 \;m\)
Top Questions on Units and measurement
- The mass of an object is measured as \( (28 \pm 0.01) \) g and its volume as \( (5 \pm 0.1) \) cm\(^3\). What is the percentage error in density?
- MHT CET - 2025
- Physics
- Units and measurement
Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter $ D $ of a tube. The measured value of $ D $ is:
- JEE Advanced - 2025
- Physics
- Units and measurement
- The number of significant figures in the measurement 0.00456 is:
- BITSAT - 2025
- Physics
- Units and measurement
- A voltmeter of resistance 1000 \( \Omega \) can measure up to 25 V. How will you convert it so that it can read up to 250 V?
- CBSE CLASS XII - 2025
- Physics
- Units and measurement
- The dimensional formula for RC is:
- CBSE CLASS XII - 2025
- Physics
- Units and measurement
Questions Asked in JEE Main exam
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
- JEE Main - 2025
- Kinetic Energy
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- permutations and combinations
- A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
- JEE Main - 2025
- Magnetic Field
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
Concepts Used:
Units and Measurement
Unit:
A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.
Measurement:
The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.
Read More: Fundamental and Derived Units of Measurement
System of Units:
- CGS system
- FPS system
- MKS system
- SI units
Types of Units:
Fundamental Units -
The units defined for the fundamental quantities are called fundamental units.
Derived Units -
The units of all other physical quantities which are derived from the fundamental units are called the derived units.