A freely body acquires a velocity of g^(x)h^(y) after falling through a height h. Using dimensions find the values fo x and y.

A freely body acquires a velocity of g^(x)h^(y) after falling through

1.	A freely body acquires a velocity of g^(x)h^(y) after falling through a height h. Using dimensions find the values fo x and y.
Answer» Solution :`v=g^(X)h^(y)` Taking dimensions on both SIDES `LT^(-1)=(LT^(-2))^(x)(L)^(y)=L^(x)T^(-2x)L^(y)=L^(x+y)T^(-2x)` EQUATING the dimensions of T and L on both sides, `-2x=-1,x=1//2, 1=x+y,y=1-1//2=1//2,x=1/2,y=1/2` SUBSTITUTING in eq (i) `v=g^(1//2)R^(1//2),v=sqrt(gh)`