The force is given in terms of time t and displacement x by the equation F=A cos B x+ C sin D t The dimensional formula of (A D/B) is:

Question

The force is given in terms of time t and displacement x by the equation F=A cos B x+ C sin D t The dimensional formula of (A D/B) is: (A) [M0 L T-1]  (B) [M L2 T-3]  (C) [M1 L1 T-2] (D) [M2 L2 T-3]

Tardigrade Admin · Accepted Answer

[A]=[M L T-2] [B]=[L-1] [D]=[T-1] [(A D/B)]=([M L T-2][T-1]/[L-1]) [(D/B)]=[M L2 T-3]

Q. The force is given in terms of time $t$ and displacement $x$ by the equation $F = A cos B x + C sin D t$ The dimensional formula of $\frac{A D}{B}$ is:

$[M^{0} L T^{- 1}]$

$[M L^{2} T^{- 3}]$

$[M^{1} L^{1} T^{- 2}]$

$[M^{2} L^{2} T^{- 3}]$

$[A] = [M L T^{- 2}]$
$[B] = [L^{- 1}]$
$[D] = [T^{- 1}]$
$[\frac{A D}{B}] = \frac{[ M L T ^{- 2} ] [ T ^{- 1} ]}{[ L ^{- 1} ]}$
$[\frac{D}{B}] = [M L^{2} T^{- 3}]$

Q. The force is given in terms of time t and displacement x by the equation F=AcosBx+CsinDt The dimensional formula of BAD​ is:

[M0LT−1]

[ML2T−3]

[M1L1T−2]

[M2L2T−3]