BITSAT2016PhysicsUnits and DimensionsActual
The frequency of vibration of string is given by v = p 2 l [ F m ]^ 1 / 2 Here p is number of segments in the string and l is the length. The dimensional formula for m will be
Options
- A[ M ⁰ LT ⁻¹ ]
- B[ ML ⁰ ~T ⁻¹ ]
- C[ ML ⁻¹ ~T ⁰ ]
- D[ M ⁰ ~L ⁰ ~T ⁰ ]
Correct answer
C. [ ML ⁻¹ ~T ⁰ ]
Step-by-step solution
v = p 2 [ F m ]^ 1 / 2 v²= p 4 ² F m m= p² F 4 ² v² Now, dimensional formula of R.H.S. = MLT ⁻² ~L ² ( 1 ~T )² [p will have no dimension as it is an integer] = ML ⁻¹ ~T ⁰ So, dimensions of m will be ML ⁻¹ ~T ⁰ .