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

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Solution

The correct option is D

In the given equation 'Bx' and 'Dt' should be dimensionless.

$\Rightarrow X = [L]$
$[B] = [L^{- 1}]$ and $[D] = [T^{- 1}]$
then $[\frac{D}{B}] = [\frac{L}{T}] = [v e l o c i t y] = [L T^{- 1}]$

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Q. The force

F

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

D / B

is.

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The force F is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt. The dimensional formula of DB is:

The correct option is D In the given equation 'Bx' and 'Dt' should be dimensionless. ⇒X=[L] [B]=[L−1] and [D]=[T−1] then [DB]=[LT]=[velocity]=[LT−1]

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

The correct option is D

In the given equation 'Bx' and 'Dt' should be dimensionless.

$\Rightarrow X = [L]$
$[B] = [L^{- 1}]$ and $[D] = [T^{- 1}]$
then $[\frac{D}{B}] = [\frac{L}{T}] = [v e l o c i t y] = [L T^{- 1}]$