MHT CET2019Evening ShiftPhysicsUnits and DimensionsActual
If ‘x’, ‘v’ and ‘a’ denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time t, then which one of the following does not change with time?
Options
- Aa T x
- Ba t + 2 π v
- Ca T v
- Da T + 4 π 2 v 2
Correct answer
C. a T v
Step-by-step solution
Key Idea for checking the correctness of an equation dimensional analysis is done using the principle of homogeneity. The dimensions of given variables of SHM are as Displacement, x = M 0 L T 0 Velocity, v = M 0 L T - 1 Acceleration, a = M 0 L T - 2 and time period, T = M 0 L 0 T Now, checking each option for these values for option (a) a T x = M 0 L T - 2 M 0 L T 0 = M 0 L 0 T - 1 As it depends on time, so change with it. For option (b), a T + 2 π v = M 0 L T - 2 M 0 L 0 T + M 0 L 0 T - 1 = M 0 L T - 1 It is also