As the physical quantity is obtained from the ratio of thermal conductivity and universal gravitational constant therefore, the dimensional formula of it is,
[k]
[G]
=
[M1L1T−3K−1]
[M−1L3T−2]
=[M2L−2T−1K−1] Compare the above dimensional formula with the given dimensional formula, [M2aL4bT2cKd]=[M2L−2T−1K−1] Thus, a=1,b=−
1
2
,c=−
1
2
and d=
1
2
The values of required expression is calculated as