Question

The distance travelled by an object, s is given by

S =at^2 + bt^3/(a+c^2)
where
t is
time.
The
dimensions of b and c respectively are​

Answer 1

Answer:

a Dimension = M⁰L¹T⁻²

b dimension = M⁰L²T⁻⁵

c Dimension =  M⁰√L T⁻¹  

Explanation:

S = at²   + bt³/(a + c²)

S = Distance  =  (Length)

so Dimension of S  = M⁰L¹T⁰

at²  & bt³/(a + c²) will have dimension of S

=> at²  Dimension = M⁰L¹T⁰

=> a Dimension = M⁰L¹T⁻²

a + c²  => c²   & a  has same dimension

=> c Dimension =  √(M⁰L¹T⁻²)  =  M⁰√L T⁻¹  

√L = (L) ^(1/2)

c Dimension =  M⁰√L T⁻¹  

bt³/(a + c²)  will have dimension of S

=> bt³/a will have dimension of S

=> bt³  = M⁰L¹T⁰  * M⁰L¹T⁻²

=> b dimension = M⁰L²T⁻⁵