If force F is related with distance x and time t as F=A√x+Bt2 , the dimensions of (A/B) is

Question

If force F is related with distance x and time t as F=A√x+Bt2 , the dimensions of (A/B) is (A) M0L- 1 / 2T (B) ML- 1 / 2T- 2 (C) M0L- 1 / 2T2 (D) M0 L T- 2

Tardigrade Admin · Accepted Answer

All terms of an equation must have same dimensions [M L T- 2]=[A L (1/2) ]=[B T2] [A]=(M L T- 2/√L) [B]=(M L T- 2/T2)

Q. If force $F$ is related with distance $x$ and time $t$ as $F = A x + B t^{2}$ , the dimensions of $\frac{A}{B}$ is

$M^{0} L^{- 1/2} T$

$M L^{- 1/2} T^{- 2}$

$M^{0} L^{- 1/2} T^{2}$

$M^{0} L T^{- 2}$

All terms of an equation must have same dimensions
$[M L T^{- 2}] = [A L \frac{1}{2}] = [B T^{2}]$

$[A] = \frac{M L T ^{- 2}}{L}$
$[B] = \frac{M L T ^{- 2}}{T ^{2}}$

Q. If force F is related with distance x and time t as F=Ax​+Bt2 , the dimensions of BA​ is

M0L−1/2T

ML−1/2T−2

M0L−1/2T2

M0LT−2

All terms of an equation must have same dimensions [MLT−2]=[AL21​]=[BT2] [A]=L​MLT−2​ [B]=T2MLT−2​