Force acting on a particle is given by F=(A - x/B t) , where x is in metre and t is in seconds. The dimensions of B is -

Question

Force acting on a particle is given by F=(A - x/B t) , where x is in metre and t is in seconds. The dimensions of B is - (A) MLT- 2 (B) M- 1T- 3 (C) M- 1T (D) MT- 1

Tardigrade Admin · Accepted Answer

F = ma, we get F=[M1] [.L1T- 2]. The dimension of force = [.MLT- 2]. [F]=([A - x]/[B] [t]) [B]=([. L ]./[M L T- 2] [. T ].)=[M- 1 T1]

Q. Force acting on a particle is given by $F = \frac{A - x}{Bt}$ , where x is in metre and t is in seconds. The dimensions of B is -

$M L T^{- 2}$

$M^{- 1} T^{- 3}$

$M^{- 1} T$

$M T^{- 1}$

F = ma, we get
$F = [M^{1}] [L^{1} T^{- 2}]$
The dimension of force = $[M L T^{- 2}]$
$[F] = \frac{[ A - x ]}{[ B ] [ t ]}$
$[B] = \frac{[ L ]}{[ M L T ^{- 2} ] [ T ]} = [M^{- 1} T^{1}]$

Q. Force acting on a particle is given by F=BtA−x​ , where x is in metre and t is in seconds. The dimensions of B is -

MLT−2

M−1T−3

M−1T

MT−1