JEE Main202431 Jan 2024Morning ShiftPhysicsUnits and DimensionsActual
A force is represented by F = a x 2 + b t 1 2 , where x = distance and t = time. The dimensions of b 2 a are :
Options
- A[ M L 3 T – 3 ]
- B[ M L T – 2 ]
- C[ M L – 1 T – 1 ]
- D[ M L 2 T – 3 ]
Correct answer
A. [ M L 3 T – 3 ]
Step-by-step solution
Given: F = a x 2 + b t 1 2 Dimension of a = F x 2 = M L T - 2 L 2 = M 1 L - 1 T - 2 Dimension of b = F t 1 2 = M L T - 2 T 1 2 = M 1 L 1 T - 5 2 Required value, b 2 a = M 2 L 2 T - 5 M 1 L - 1 T - 2 = M 1 L 3 T - 3