Answer:
Solution given:
t=[tex]2π \sqrt{\frac{m}{g}}[/tex]
where
t=time and it's dimension is [T¹]
m=mass and its dimension is [M¹]
dimension of constant term is nothing.
t=[tex]2π \sqrt{\frac{m}{g}}[/tex]
squaring on both side
we get
t²=4π²*[tex]\frac{m}{k}[/tex]
since 4π² has no dimension
Dimension of t²=[T²]
Dimension of m=[M¹]
Dimension of k=?
By using
The principle of homogeneity of dimension we get
Dimension of t²=dimension of [tex]\frac{m}{k}[/tex]
[T²]=[tex]\frac{[M¹]}{K}[/tex]
doing crisscrossed multiplication
K=[tex]\frac{[M¹]}{[T²]}[/tex]
dimension of k is[tex] [M¹T^{-2}] [/tex]or [tex][M¹L^0T^{-2}][/tex]
since length is absent
