Question

If x is equal to 2at -5 bt square x is in metre and team second then find the dimensions of a and b

Answer 1

Answer:

[a] = m/s ; [b] = m/s^2

Step-by-step explanation:

[x] = [L] = m

[x] = [L] = m[t] = [T] = sec

We can add only terms with same dimensions,

We can add only terms with same dimensions,Hence, since --

$x = 2at - 5bt {}^{2}$

==> 2at = x

[a] = [x/2t] = m/s

{ constants like 2 are dimensionless }

And,

5bt^2 = [x]

[b] = [x / 5t^2 ]= m/s^2

{ constants like 5 are dimensionless }

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Hope it helps....!

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Answer 2

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Given :-

x = 2at - 5bt²

if x is in meter

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To Find :-

Dimensions of a and b

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Solution :-

If,

x = 2at² - 5bt²

Then,

$\Large{\sf{x \: = \: 2at}}$

$\Large \leadsto {\sf{a \: = \: \frac{x}{t}}}$

As Constants are Dimensional less.

$\LARGE \implies {\boxed{\boxed{\sf{a \: = \: [M^0 L^1 T^{-1}}}}}$

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Similarly,

$\Large{\sf{x \: = \: -5bt^2}}$

$\Large \leadsto {\sf{b \: = \: \frac{x}{t^2}}}$

[5 is also dimensional less as it is a constant ]

$\LARGE \implies {\boxed{\boxed{\sf{b \: = \: M^0 L^1 T^{-2}}}}}$