COMEDK2014PhysicsUnits and Dimensions
Which two of the following quantities are dimensionally equivalent?
Options
- A(i) and (ii)
- B(i) and (iii)
- C(ii) and (iii)
- D(ii) and (iv)
Correct answer
C. (ii) and (iii)
Step-by-step solution
We know that, Force = Mass Acceleration F=m a [F]=[ m ][ a ]=[ M ] [ LT ⁻² ]= [ MLT ⁻² ] Pressure (p)= Force (F) Area (A) [p]= [ F ] [ A ] = [ MLT ⁻² ] [ L ² ] = [ ML ⁻¹ ~T ⁻² ] Young's modulus, Y= Stress Strain [Y]= [ Stress ] [ Strain ] = [F / A] [ Strain ] = [ ML ⁻¹ ~T ⁻² ] [ M ⁰ ~L ⁰ ~T ⁰ ] = [ ML ⁻¹ ~T ⁻² ] Energy = Work done = Force Displacement [ Energy ]=[ Force ] [ Displacement ]= [ MLT ⁻² ][ L ]= [ ML ² ~T ⁻² ] Hence, we see that dimensions of pressure and Young's modulus is same.