BITSAT2013PhysicsUnits and DimensionsActual
Wave pulse can travel along a tense string like a violin spring. Aseries of experiments showed that the wave velocity V of a pulse depends on the following quantities, the tension T of the string, the cross-section area A of the string and then as per unit volume of the string. Obtain an expression for V in terms of the T , A and using dimensional analysis.
Options
- AV = k T A
- BV = k T A
- CV=k A T
- DNone of these
Correct answer
A. V = k T A
Step-by-step solution
Let V = kT ^ a A ^ b ^ c , k = dimensional constant Writing dimension on both we side aligned [ LT ⁻¹ ] &= [ MLT ⁻² ]^ a [ ~L ² ]^ b [ ML ⁻³ ]^ c &= [ M ^ a + c L ^ a +2 ~b -3 c T ^ -2 a ] aligned Comparing power on both sides we have array l a+c=0, a+2 b-3 c=1, -2 a=-1 a= 1 2 , c=- 1 2 b=- 1 2 V=k T A array