A physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula [M2 a L4 b T2 c Kd], then the value of (a+b/c+b)-d is

Question

A physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula [M2 a L4 b T2 c Kd], then the value of (a+b/c+b)-d is (A) +(3/2) (B) -(1/2) (C) -(3/2) (D) +(1/2)

Tardigrade Admin · Accepted Answer

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,

\frac{[ 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 = - \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}

Q. 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 $\frac{a + b}{c + b} - d$ is

$+ \frac{3}{2}$

$- \frac{1}{2}$

$- \frac{3}{2}$

$+ \frac{1}{2}$

Q. A physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula [M2aL4bT2cKd], then the value of c+ba+b​−d is

+23​

−21​

−23​

+21​

Q. 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 $\frac{a + b}{c + b} - d$ is

$+ \frac{3}{2}$

$- \frac{1}{2}$

$- \frac{3}{2}$

$+ \frac{1}{2}$