If v=(A/t)+Bt2+Ct3 where v is velocity, t is time and A, B and C are constants, then the dimensional formula of B is

Question

If v=(A/t)+Bt2+Ct3 where v is velocity, t is time and A, B and C are constants, then the dimensional formula of B is (A) [.M0LT0]. (B) [.ML0T0]. (C) [.M0L0T ]. (D) [.M0LT- 3].

Tardigrade Admin · Accepted Answer

Dimension of velocity = [.M0L1T- 1]. [. v ]. = [. B t2 ]. ∴ [. B ]. = ([. v ]./[. t2 ].) = ([. textM0 textL1 textT- 1 ]./[. textT2 ].) = [. textL1 textT- 3 ].

Q. If $v = \frac{A}{t} + B t^{2} + C t^{3}$ where $v$ is velocity, $t$ is time and $A, B$ and $C$ are constants, then the dimensional formula of $B$ is

$[M^{0} L T^{0}]$

$[M L^{0} T^{0}]$

$[M^{0} L^{0} T]$

$[M^{0} L T^{- 3}]$

Dimension of velocity = $[M^{0} L^{1} T^{- 1}]$
$[v] = [B t^{2}]$
$∴ [B] = \frac{[ v ]}{[ t ^{2} ]} = \frac{[ M ^{0} L ^{1} T ^{- 1} ]}{[ T ^{2} ]} = [L^{1} T^{- 3}]$

Q. If v=tA​+Bt2+Ct3 where v is velocity, t is time and A,B and C are constants, then the dimensional formula of B is

[M0LT0]

[ML0T0]

[M0L0T]

[M0LT−3]