Question

The velocity of a particle depends upon t according to the equation v=a+bt+c/(d+t). Write the dimensions of a,b,c and d

Answer 1

GiveN :

• v = (a + bt + c)/d + t

To FinD :

• Dimensions of a,b,c and d

SolutioN :

We know that :

$\boxed{\sf{v \: = \: [LT^{-1}]}}$

$\rule{150}{0.5}$

By the equation :

$\rightarrow \sf{v \: = \: a} \\ \\ \rightarrow \sf{a \: = \: [M^0 LT^{-1}]}$

• Dimension of a is $\sf{[M^0 LT^{-1}]}$

$\rule{150}{0.5}$

$\rightarrow \sf{v \: = \: bt} \\ \\ \rightarrow \sf{[LT^{-1}] \: = \: [T] b} \\ \\ \rightarrow \sf{b \: = \: \dfrac{[LT^{-1}]}{[T]}} \\ \\ \rightarrow \sf{b \: = \: [LT^{-2}]}$

• Dimension of b is $\sf{[M^0LT^{-2}]}$

$\rule{150}{0.5}$

$\rightarrow \sf{v \: = \: c} \\ \\ \rightarrow \sf{c \: = \: [LT^{-1}]}$

• Dimension of c is $\sf{[LT^{-1}]}$

$\rule{150}{0.5}$

As, we know that only two similar quantities can be added. And we are given, d + t

• So, Dimension to d is $\sf{[M^0 L^0 T]}$