Hydrostatic pressure P varies with displacement - x- as p- A B log Bx 2 -c where A- B and C are constants- The dimensional formula for - A- is-

Potential energy U varies with distance x as $U = \frac{A x^{1 / 2}}{X^{2} + B}$ where A and B are constant. The dimensional formula for $A \times B$ is

Q. What are the dimensions of

a

and

b

in the relation

F = a \sqrt{x} + b t^{2}

where

F

is force,

x

is distance and

t

is time?

Q. If kinetic energy of a body is given as

k = C x

where

C

is constant and

x

is distance from origin then, dimensional formula for

C

Join BYJU'S Learning Program

Hydrostatic pressure P varies with displacement 'x' as p=ABlog(Bx2+c) where A,B and C are constants. The dimensional formula for 'A' is:

The correct option is D ML−3T−2P=ABlog(Bx2+c)Bx2 should be dimensionless ⇒B=L−2⇒AB=M1L−1T−2⇒A=(M1L−1T−2)(L−2)⇒A=M1L−3T−2

Hydrostatic pressure $P$ varies with displacement ' $x$ ' as $p = \frac{A}{B} l o g ({B x}^{2} + c)$ where $A, B$ and $C$ are constants. The dimensional formula for ' $A$ ' is:

The correct option is D ${M L}^{- 3} T^{- 2}$
$P = \frac{A}{B} l o g (B x^{2} + c)$
$B x^{2}$ should be dimensionless $\Rightarrow B = L^{- 2}$
$\Rightarrow \frac{A}{B} = M^{1} L^{- 1} T^{- 2}$
$\Rightarrow A = (M^{1} L^{- 1} T^{- 2}) (L^{- 2})$
$\Rightarrow A = M^{1} L^{- 3} T^{- 2}$