Question

find the dimensions of the constants a , b, c and d in the relation v = a +bt + c/d+t where v is velocity and t is time.

Answer 1

Answer:

I hope this helps u...

Answer 2

Answer:

The dimensions of the constants a, b, c, and d are [M⁰LT⁻¹], [M⁰LT⁻²],[T], and [M⁰LT⁰].

Explanation:

The given equation is of the form,

$v=a+bt+\frac{c}{d+t}$     (1)

Now let's find the dimensions one by one.

For "a"

$[a]=[v]$     (2)

The dimensions of velocity are =[M⁰LT⁻¹]

So,

$[a]=[M^0LT^-^1]$      (3)

For "b"

$[bt]=[v]$

So,

$[bT]=[M^0LT^-^1]$

$[b]=[M^0LT^-^2]$     (4)

For "d"

As dimensionally equal values are added together so the dimensions of d will be the same as that of time i.e.

$[d]=[T]$    (5)

For 'c'

$\frac{[c]}{[d+t]}=[v]$

So,

$\frac{[c]}{[T]}=[M^0LT^-^1]$

$[C]=[M^0LT^-^1][T]$

$[C]=[M^0LT^0]$   (6)

Hence, the dimensions of the constants a, b, c, and d are [M⁰LT⁻¹], [M⁰LT⁻²],[T], and [M⁰LT⁰].

#SPJ2