Question

if f=ax+bt²+c where f is force x is distance, t is time then what is dimension of axc/bt²​

Answer 1

Given : -

f = ax + bt² + c; where f is force, x is distance and t is time.

To Find : -

Dimension of ac/bt²

Solution : -

Only like quantities having same dimensions can be added to or subtracted from each other.

1. Dimension of 'a' : -

→ [f] = [a] [x]

→ [M¹L¹T‾²] = [a] [L¹]

→ [a] = [M¹T‾²]

2. Dimension of 'b' :-

→ [f] = [b] [t²]

→ [M¹L¹T‾²] = [b] [T²]

→ [b] = [M¹L¹T‾⁴]

3. Dimension of 'c' : -

→ [f] = [c]

→ [c] = [M¹L¹T‾²]

Dimension of ac/bt² :

➛ [a] [c] / [b] [t²]

➛ [M¹T‾²] [M¹L¹T‾²] / [M¹L¹T‾⁴] [T²]

➛ [M²L¹T‾⁴] / [M¹L¹T‾²]

➛ [M¹T‾²]