It is confusing me a bit... My answer is coming really veery different.. help..

Asked by nitishkrnehu09 | 23rd Nov, 2017, 10:16: AM

Expert Answer:

The given equation begin mathsize 12px style V left parenthesis x right parenthesis space equals space minus alpha x plus beta space sin left parenthesis space bevelled x over gamma space right parenthesis end style
let us assume x has dimension of length, i.e. m
Since dimension of V(x) is joules, dimension of α is N (Newton, force unit)
Argument of sine function does not have unit. Hence unit of β is joules and unit of γ is m-1  
 
if we analyze different combination (A)  :-  begin mathsize 12px style open square brackets fraction numerator begin display style alpha end style over denominator begin display style beta gamma end style end fraction close square brackets space equals space fraction numerator N over denominator J o u l e s cross times m to the power of negative 1 end exponent end fraction space equals space fraction numerator N over denominator N cross times m cross times m to the power of negative 1 end exponent end fraction space equals space u n i t l e s s space c o m b i n a t i o n end style
if you workout the dimensional analysis for other combinations, you will not get the end result as unitless combination.
 
Hence option(A) is the correct answer

Answered by  | 4th Dec, 2017, 11:55: AM