AP EAMCET202420 May 2024Evening ShiftPhysicsUnits and DimensionsActual
Find the dimension formula of a b in the equation F=a x +b t^2 , where F is a force, x is distance and t is time.
Options
- A[M^0 L^ -1 / 2 T^2 ]
- B[M^0 L^0 T^ 3 / 2 ]
- C[M^0 L^1 T⁻⁴ ]
- D[M^0 L^ -3 / 2 T^4 ]
Correct answer
A. [M^0 L^ -1 / 2 T^2 ]
Step-by-step solution
F=a x +b t^2 By principle of homogeneity aligned & [ F ]=[ a x ] [ a ]= [ F ] [ x ] & [ F ]= [ bt ^2 ] [ b ]= [ F ] [ t ^2 ] aligned aligned [ a b ]= [ F ] [ x ] [ t ^2 ] [ F ] & = [ t ^2 ] [ 1 1 2 ] = [ T ^2 ] [ 1 ~L ^2 ] & = [ M ^0 ~L ^ -1 / 2 ~T ^2 ] aligned