Question

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

• A. $+\frac{3}{2}$
• B. $-\frac{1}{2}$
• C. $-\frac{3}{2}$
• D. $+\frac{1}{2}$

Answer 1

Answer: (D)

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