Question

let x=a+bt+ct2 where x is an meter and t in second what will be the dimension of a,b and c?​

Answer 1

$\bf\huge\underline{\underline{ Given :- }}$

• x = a + bt + ct²

• x is in metre .

• t is in second

$\bf\huge\underline{\underline{ To \: Find:- }}$

• dimensions of a , b and c

$\bf\huge\underline{\underline{ Answer :- }}$

• dimension of length = [ L ]

• dimension of time = [ T ]

since x is in metre , dimension of x

• $\red{\implies}$ x = [ L ]

$\rule{10cm}{0.0005cm}$

• dimensions of a , bt , ct² will be [ L ]

• a = [ L ]

$\rule{10cm}{0.00005cm}$

• bt = [ L ]

• $\red{\implies}$ b = $\sf \frac{[ L ] }{t}$

• $\red{\implies}$ b = $\sf \frac{[ L ] }{[ T ] }$

• $\red{\implies}$ b = $\sf [ LT^{-1} ]$

$\rule{10cm}{0.0005cm}$

• ct² = [ L ]

• $\red{\implies}$ c = $\sf \frac{ [ L ] }{ t² }$

• $\red{\implies}$ c = $\sf \frac{ [ L ] }{ [ T² ] }$

• $\red{\implies}$ c = $\sf [ LT^{-2} ]$

$\rule{10cm}{0.05cm}$

ie ,

• dimension of a = $\sf [ L ]$

• dimension of b = $\sf [ LT^{-1} ]$

• dimension of c = $\sf [ LT^{-2} ]$

$\rule{10cm}{0.05cm}$

Answer 2

Answer:

I Hope it's help you