Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation
The gravitational potential in a certain region is given by V = 20 N/kg , (x + y) , where x and y represent spatial coordinates in meters. What is the dimensional formula of the gravitational potential V ?
Options
- A[L^2 T⁻²]
- B[M L^2 T⁻²]
- C[L T⁻²]
- D[M L T⁻¹]
Correct answer
A. [L^2 T⁻²]
Step-by-step solution
Gravitational potential V is defined as the work done per unit mass. V = W m The dimensional formula for work W is [M L^2 T⁻²] and for mass m is [M] . Substituting these dimensions, we get: [V] = [M L^2 T⁻²] [M] = [L^2 T⁻²] Alternatively, from the given equation, the unit of V is ( N/kg ) m = J/kg . The dimensional formula for Joule is [M L^2 T⁻²] and for kg is [M] . Thus, [V] = [M L^2 T⁻²] [M] = [L^2 T⁻²]