A physical quantity x is represented by the f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given formula is $x = M^a L^b T^c$. Dimensional analysis states that if a quantity depends on $M, L,$ and $T$,it can be expressed in terms of

Vedclass · Accepted Answer

The dimension of $x$ cannot be expressed in terms of $M$ and $L$.

Vedclass · Answer

(B) The given formula is $x = M^a L^b T^c$. Dimensional analysis states that if a quantity depends on $M, L,$ and $T$,it can be expressed in terms of $M$ and $L$ only if the exponent of $T$ is zero (i.e.,$c = 0$). If $c 
eq 0$,the quantity $x$ essentially depends on the dimension of time $T$. Therefore,if $c 
eq 0$,the dimension of $x$ cannot be expressed solely in terms of $M$ and $L$ because the contribution of $T$ cannot be ignored or substituted by $M$ and $L$ unless there is a specific physical relationship between them.

$A$ physical quantity $x$ is represented by the formula $x = M^a L^b T^c$. If $c \neq 0$,then:

Similar Questions

The density of a material in $SI$ units is $128 \ kg \ m^{-3}$. In a system of units where the unit of length is $25 \ cm$ and the unit of mass is $50 \ g$,the numerical value of the density of the material is:

If velocity $v$,acceleration $A$,and force $F$ are chosen as fundamental quantities,then the dimensional formula of angular momentum in terms of $v, A$,and $F$ would be

If $A, B$ and $C$ are three different physical quantities with different dimensional formulae, then the combination which can never give a proper physical quantity is

The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?

$E, m, L, G$ represent energy,mass,angular momentum,and gravitational constant respectively. The dimensions of $\frac{EL^2}{m^5 G^2}$ will be that of

Vedclass Test Series

Exam Paper Generator

Online Exam Module