In the expression P=El^(2)m^(-5)G^(-2),Em,l and Gdenote energy, mass, angular momentum and gravitational constant respectively. Show that P is a dimensionless quantity.

In the expression P=El^(2)m^(-5)G^(-2),Em,l and Gdenote energy, mass,

1.	In the expression P=El^(2)m^(-5)G^(-2),Em,l and Gdenote energy, mass, angular momentum and gravitational constant respectively. Show that P is a dimensionless quantity.
Answer» SOLUTION :Givet, expression is `P=EL^(2)m^(-5)G^(-2)` where E is ENERGY `[E]=[M^(1)L^(2)T^(-2)]` m is mass `[m]=[M^(1)]` L is angular moment`[L][M^(1)L^(2)T^(-1)]` G is gratvittional constant `[G]=[M^(1)L^(3)T^(-2)]` Substituting DIMENSIONS of each term in the given expression `[P]=[M^(1)L^(2)T^(-2)]xx[M^(1)L^(2)T^(-1)]xx[M^(1)]^(-5)xx[M^(-1)L^(3)T^(-2)]^(-2)` `=[M^(1+2-5+2)L^(2+4-6)T^(-2-2+4)]=[M^(0)L^(0)T^(0)]` Hence P is a dimensionless QUANTITY.