A force F is given by F = at + bt2 where t is time, what are the dimension of a and b.

  1. MLT1, MLT0
  2. MLT3, ML2T4
  3. MLT-4, MLT-4
  4. MLT-3, MLT-4

Answer (Detailed Solution Below)

Option 4 : MLT-3, MLT-4
Free
Agniveer Navy SSR Full Test - 01
4 K Users
100 Questions 100 Marks 60 Mins

Detailed Solution

Download Solution PDF

CONCEPT:

Principle of homogeneity of dimensions:

  • According to this principle, a physical equation will be dimensionally correct if the dimensions of all the terms occurring on both sides of the equation are the same.
  • This principle is based on the fact that only the physical quantities of the same kind can be added, subtracted, or compared.
  • Thus, velocity can be added to velocity but not to force.

 

EXPLANATION

Given - F = at + bt2

From the principle of dimensional homogeneity, the left-hand side of the equation dimensionally equal to the right-hand side of the equation.

The dimension formula of force (F) = [MLT-2]

∴ [MLT-2] = [a] [T]

\(⇒ \left[ a \right] = \frac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ T \right]}} = \left[ {ML{T^{ - 3}}} \right]\)

For second term,

⇒ [MLT-2] = [b] [T2]

\(\Rightarrow \left[ b \right] = \frac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ {{T^2}} \right]}} = \left[ {ML{T^{ - 4}}} \right]\)

Latest Indian Navy Agniveer SSR Updates

Last updated on May 31, 2025

-> The Indian Navy SSR Agniveeer Merit List will be released soon on the official website.

-> The Indian Navy Agniveer SSR CBT Exam was conducted from 25th to 26th May 2025.

->The application window was open from 29th March 2025 to 16th April 2025.  

-> The Indian Navy SSR Agniveer Application Link is active on the official website of the Indian Navy.

.->Only unmarried males and females can apply for Indian Navy SSR Recruitment 2025.

-> The selection process includes a Computer Based Test, Written Exam, Physical Fitness Test (PFT), and  Medical Examination.

->Candidates Qualified in 10+2 with Mathematics & Physics from a recognized Board with a minimum 50% marks in aggregate can apply for the vacancy.

-> With a salary of Rs. 30,000, it is a golden opportunity for defence job seekers.

-> Candidates must go through the Indian Navy SSR Agniveer Previous Year Papers and Agniveer Navy SSR mock tests to practice a variety of questions for the exam.

Get Free Access Now
Hot Links: teen patti master 2023 teen patti master official teen patti lotus