Question

If the dimensional formula of a physical quantity is
given by [M^x L^y T^z] then the physical quantity will be
(1) Torque, if x = 1, y = 2 and z = 2
(2) Surface tension, if x = 1, y = 0 and z = -2
(3) Work, it x = 1, y = 1 and z = -2
(4) Velocity. if x = 0, y = 1 and z = 2​

Answer 1

(2). Surface tension

As Dimensional Formula Of Surface tension = $M {T}^{ - 2}$

So Surface tension =$M {L}^{0} {T}^{-2}$

And This is possible when X=1 , y=0 and Z=-2

Thanks for asking.

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

Dimensional formula given:-

$\large{\bold{M^{x} L^{y} T^{z}}}$

$\huge{\bold{\underline{Explanation:-}}}$

Let's verify each option.

Case-1

$\large{\bold{ \vec{ \tau} = \vec{F} \times \vec{r}}}$

Now, Dimensions.

$\large{ \implies \vec{ \tau} = MLT^{-2} \times L}$

$\large{\boxed{\boxed{ \implies \vec{ \tau} = ML^{2}T^{-2}}}}$

Comparing with the given values in question.

$\large{\bold{x = 1 \: y = 2 \: z = -2}}$

So, this option is correct.

Case-2

Surface tension is denoted by ${ \eta}$

$\large{\bold{ \eta = \frac{Force}{Length}}}$

Now,Dimensions

$\large{ \implies \eta = \frac{MLT^{-2}}{L}}$

$\large{ \implies \eta = \frac{M \cancel{L}T^{-2}}{ \cancel{L}}}$

$\large{\boxed{\boxed{ \implies \eta = ML^{0}T^{-2}}}}$

Comparing with the given values in question.

$\large{\bold{x = 1 \: y = 0 \: z = -2}}$

So,this option is correct.

Case-3

$\large{\bold{ W = F.S}}$

Now,Dimensions

$\large{ \implies W = MLT^{-2} \times L}$

$\large{\boxed{\boxed{ \implies W = ML^{2}T^{-2}}}}$

Comparing with the given values in question.

$\large{\bold{x = 1 \: y = 2 \: z = -2}}$

This condition doesn't matches.

So,this option is wrong.

Case-4

$\large{\bold{V = \frac{Distance}{Time}}}$

Now,Dimensions

$\large{ \implies V = \frac{L}{T}}$

$\large{\boxed{\boxed{ \implies V = M^0L^1T^{-1}}}}$

Comparing with the given values in question.

$\large{\bold{x = 0 \: y = 1 \: z = -1}}$

This condition doesn't matches.

So,this option is wrong.

So,the option 1 and 2 are correct.