Question

If x=at+bt2 where x is the distance travelled and t is time then the dimensions of b is___________

Answer 1

$\rm \underline \purple{Topic:-}$

Units and Dimensions

$\rm \underline \purple{Given \: to \: find \: the \: dimensions \: of \: b:-}$

where,

x = at + b²

Explanation:-

Here the principle of Homogeneity of Dimensions be used :-

x = at + bt²

Where,

• x = Distance travelled
• t = time taken

As we need to find the Dimensions of b

According to that law :-

x = bt²

So,

$\rm \: b = \dfrac{x}{t {}^{2} }$

Finding the Dimensions of x, t²

x = Distance travelled

x = [L]

t² = [T]²

So,

$\rm \: b = \dfrac{x}{T {}^{2} }$

$\rm \: b = \dfrac{ [ \ \: L] \ }{[ \ \: T {}^{2} ]}$

$\rm \: b = [ \ \: LT {}^{ - 2} ]$

So, the dimensional formula of b is [LT^-2]

_____________________

What the Principal of Homogeneity of Dimensions tells us ?

If x= y+z dimensionally correct and if x represents the physical quantity, then y and z also must represent the same physical quantity . It means that the terms on both sides of dimensional equation should have same dimensions . This is called Principal of Homogeneity of Dimensions .

Answer 2

Answer:

The dimensional of b is [LT⁻²].

Explanation:

x = at + bt²

Where,

x = Distance travelled

t = time taken

According to the law of the Principle of Homogeneity of Dimensions:-

x = bt²

So,

the Dimensions of x, t²

x = Distance travelled

t = time taken

Dimensions of x = [L]

Dimensions of t² = [T]²

So, x = b t²

b =  x / t²

b = [ L ]  / [ T ²]

b =  [ LT⁻²]

therefore the dimensional formula of b = [LT⁻²].

Principle of Homogeneity of Dimensions:  If x= y+z is dimensionally correct and if x represents the physical quantity, then y and z also must represent the same physical quantity. It means that the terms on both sides of the dimensional equation should have the same dimensions.

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