Question

Q. Test if the following equations are dimensionally correct (answer me in brief){I want detailed explanation}

${\huge \: v = \frac{1}{2\pi} \sqrt{ \frac{m \: g \: l \: \: }{I} } }$
​

Answer 1

Answer:

fXY(x,y) =∫

∞

−∞

fXYZ(x,y,z)dz =∫

1

0

1

3

(x+2y+3z)dz =

1

3

[(x+2y)z+

3

2

z2]

1

0

=

1

3

(x+2y+

3

2

), for0≤x,y≤1.

Thus,

fXY(x,y)={

1

3

(x+2y+

3

2

) 0≤x≤1,0≤y≤1 0