
If the unit of force is kN, the length is 1 km and for the time it is 100s, then what will be the unit of mass?
(A) 1000 kg
(B) 1 kg
(C) 10000 kg
(D) 100 kg
Answer
154.2k+ views
Hint: We know the standard SI unit of force is newtons (N), for length it is meters (m) and for time it is seconds (s). Now we are given that the unit of force is to be kilo Newton, for length it is 1km and for time it is 100s. we can make use of dimensional analysis to solve this problem.
Complete step by step solution:
We know force is given by the formula, $F=ma$
\[F=[ML{{T}^{-2}}]\]
$\Rightarrow 1000N=\dfrac{M\times 1000m}{{{(100s)}^{2}}} \\
\Rightarrow M=10000kg \\$
So, the correct option is (c)
Additional Information: Method of Dimensional analysis is also called Factor Label Method. The method of dimensional analysis is of great use as we can check the correctness of Physical Equation by using it. However, it should be kept in mind that dimensional analysis cannot help us determine any dimensionless constants in the equation. The method when used in chemistry there in place of using designated symbols we use units.
Note: There are few drawbacks for this method, although this method is widely used. This method cannot be used when we are dealing with the dimensionless quantities. Constant proportionality cannot be determined by this method. It does not apply to trigonometric, logarithmic and exponential functions physical quantities which are dependent upon more than three physical quantities, this method will be difficult.
Complete step by step solution:
We know force is given by the formula, $F=ma$
\[F=[ML{{T}^{-2}}]\]
$\Rightarrow 1000N=\dfrac{M\times 1000m}{{{(100s)}^{2}}} \\
\Rightarrow M=10000kg \\$
So, the correct option is (c)
Additional Information: Method of Dimensional analysis is also called Factor Label Method. The method of dimensional analysis is of great use as we can check the correctness of Physical Equation by using it. However, it should be kept in mind that dimensional analysis cannot help us determine any dimensionless constants in the equation. The method when used in chemistry there in place of using designated symbols we use units.
Note: There are few drawbacks for this method, although this method is widely used. This method cannot be used when we are dealing with the dimensionless quantities. Constant proportionality cannot be determined by this method. It does not apply to trigonometric, logarithmic and exponential functions physical quantities which are dependent upon more than three physical quantities, this method will be difficult.
Recently Updated Pages
JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
If the unit of power is 1Kilo Watt the length is 100m class 11 physics JEE_Main

Which of the following statements is correct if the class 11 physics JEE_Main

The quantity of heat required to heat one mole of a class 11 physics JEE_Main

IIIT JEE Main Cutoff 2024

Photoelectric Effect and Stopping Potential with Work Function and Derivation for JEE

Newton’s Laws of Motion: Three Laws of Motion Explanation with Examples

Other Pages
JEE Advanced 2025 Revision Notes for Mechanics

Ideal and Non-Ideal Solutions Raoult's Law - JEE

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

A boy wants to throw a ball from a point A so as to class 11 physics JEE_Main

List of Fastest Century In IPL - Cricket League and FAQs

NEET 2025: All Major Changes in Application Process, Pattern and More
