Question

Suppose the displacement of a particle is related to a time
according to expression S = ct. What are the dimensions of
the constant c.​

Answer 1

Answer:

Dimensions should be same in both sides.

Explanation:

S=ct

Here dimension of S is

${m}^{0} {l}^{1} {t}^{0}$

On other side

dimension is

${m}^{0} {l}^{0} {t}^{1} \\ so \: to \: make \: equal \: in \: dimension \\ c \: should \: be \\ {m}^{0} {l}^{1} {t}^{ - 1}$

Hope it will help you!!

Answer 2

dimensions of the 2 equations have to be same or else the equality won't exist

dimension of S=[M⁰L¹T⁰]

dimension of t=[M⁰L⁰T¹]

therefore dimensions of c are

=dimension of S /dimension of t

=[M⁰L¹T⁰]/[M⁰L⁰T¹]

=[M⁰L¹T⁻¹]

hope this helps