The velocity v of a particle at time t is given by v=at+(b/t+c) , where a, b and c are constants. The dimensions of a, b and c are, respectively,

Question

The velocity v of a particle at time t is given by v=at+(b/t+c) , where a, b and c are constants. The dimensions of a, b and c are, respectively, (A) [LT-2], [L] and [T] (B) [L2], [T] and [LT2] (C) [LT2], [LT] and [L] (D) [L], [LT] and [T2]

Tardigrade Admin · Accepted Answer

v=a t+(b/t+c) As c is added to t, ∴ [c]=[ T ] [a t]=[ LT -1] or, [a]=([ LT -1]/[ T ])=[ LT -2] ([b]/[ T ])=[ LT -1] ∴[b]=[ L ] .

Q. The velocity $v$ of a particle at time $t$ is given by $v = a t + \frac{b}{t + c}$ , where $a$ , $b$ and $c$ are constants. The dimensions of $a$ , $b$ and $c$ are, respectively,

$[L T^{- 2}]$ , $[L]$ and $[T]$

$[L^{2}]$ , $[T]$ and $[L T^{2}]$

$[L T^{2}]$ , $[L T]$ and $[L]$

$[L]$ , $[L T]$ and $[T^{2}]$

$v = a t + \frac{b}{t + c}$
As $c$ is added to $t,$
$∴ [c] = [T]$
$[a t] = [L T^{- 1}]$
or, $[a] = \frac{[ L T ^{- 1} ]}{[ T ]} = [L T^{- 2}]$
$\frac{[ b ]}{[ T ]} = [L T^{- 1}]$
$∴ [b] = [L]$ .

Q. The velocity v of a particle at time t is given by v=at+t+cb​ , where a, b and c are constants. The dimensions of a, b and c are, respectively,

[LT−2], [L] and [T]

[L2], [T] and [LT2]

[LT2], [LT] and [L]

[L], [LT] and [T2]