Question

A body exerted a force F which is depend upon mass m and acceleration a of that body. Then find the relation between F,m and a by using dimensional method.

Answer 1

Answer:

Newton's first law of motion predicts the behavior of objects for which all existing forces are balanced

Answer 2

Solution -

F = force = [M L T¯²]

m= mass = [M]

a= acceleration =[L T¯²]

F is directly proportional to m^x a^y

=> F= k m^x a^y - - - - - - - - - (1)

Using dimensional method,

=> [M L T¯²]=[M]^x [L T¯²]^y

=> [M L T¯²] = M ^x L^y T¯²y

Using principle of homogeneity

M¹= M^x

x=1

y=1

If k=1

Then F=ma