Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
Consider an attractive nuclear force acting between two protons that can be expressed as F = Ce^ -kr /r^2 . Determine the dimensional formulae and appropriate SI units of C and k .
Options
- A[M L^3 T⁻²] , [L] , N m ^2 , m
- B[M L^3 T⁻²] , [L⁻¹] , N m ^2 , m ⁻¹
- C[M L T⁻²] , [L⁻¹] , N , m ⁻¹
- D[M L^2 T⁻²] , [L⁻²] , J , m ⁻²
Correct answer
B. [M L^3 T⁻²] , [L⁻¹] , N m ^2 , m ⁻¹
Step-by-step solution
The given equation is F = C e^ -kr r^2 . Since the exponent of an exponential function must be dimensionless, the term kr is dimensionless. [k][r] = [M^0 L^0 T^0] [k] = 1 [r] = [L⁻¹] The SI unit of k is m ⁻¹ . The exponential term e^ -kr is dimensionless, so the dimensions of F and C r^2 must be the same. [F] = [C] [r^2] [C] = [F][r^2] = [M L T⁻²][L^2] = [M L^3 T⁻²] The SI unit of C is N m ^2 .