NEET2019PhysicsUnits and DimensionsActual
What is dimensions of energy in terms of linear momentum (P), area (A) and Time (T)
Options
- A[ P ^1 ~A ^1 ~T ^1 ]
- B[ P ^2 ~A ^2 ~T ⁻¹ ]
- C[ P ^1 ~A ^ 1 / 2 ~T ⁻¹ ]
- D[ P ^ 1 / 2 A^ 1 / 2 T⁻¹ ]
Correct answer
C. [ P ^1 ~A ^ 1 / 2 ~T ⁻¹ ]
Step-by-step solution
Dimensions of energy in terms of momentum (P). Area (A) and Time (T), is related of E = P ^ a A ^ b T ^ C (i) Writing dimensional formula of both side, aligned & [ ML ^2 ~T ⁻² ]= [ MLT ⁻¹ ]^a [L^2 ]^b[ ~T ]^ c & [ ML ^2 ~T ^ -2] ]= [ M ^ a L ^ a + T ^ - a + c ] & aligned Comparing the exponents, a =1, a +2 ~b =2 gathered 2 ~b =1 ~b = 1 2 - a + c =-2-1+ c =-2 C =-1 gathered Form Eq. (i), we have E = [ PA ^ 1 / 2 ~T ⁻¹ ]