A physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula [ M ^ 2 a ~L ^ 4 b ~T ^ 2 c ~K ^d ] , then the value of a+b c+b -d is

Step-by-step solution

Dimensional formula of thermal conductivity [k]= [ M ^1 ~L ^1 ~T ⁻³ ~K ⁻¹ ]. Dimensional formula of universal gravitational constant, [G]= [ M ⁻¹ ~L ^3 ~T ⁻² ] Now, [k] [G] = [ M ^2 ~L ⁻² ~T ⁻¹ ~K ⁻¹ ] Compare above equation with [ M ^ 2 a ~L ^ 4 b ~T ^ 2 c ~K ^d ] This will give us, a=1, b=- 1 2 , c=- 1 2 and d=-1 Now, a+b c+b -d= 1- 1 2 - 1 2 - 1 2 -(-1) or a+b c+b -d= 1 2