Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following
Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following
- A
Thrust
- B
Pressure
- C
Angle
- D
Viscosity
Similar Questions
Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$ : Time period of oscillation of a liquid drop depends on surface tension $(S)$, if density of the liquid is $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.
Reason $(R)$: Using dimensional analysis we get $R.H.S.$ having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.
Assertion $(A)$ : Time period of oscillation of a liquid drop depends on surface tension $(S)$, if density of the liquid is $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.
Reason $(R)$: Using dimensional analysis we get $R.H.S.$ having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.
- [JEE MAIN 2022]
Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
Consider following statements
$(A)$ Any physical quantity have more than one unit
$(B)$ Any physical quantity have only one dimensional formula
$(C)$ More than one physical quantities may have same dimension
$(D)$ We can add and subtract only those expression having same dimension
Number of correct statement is
The $SI$ unit of energy is $J=k g\, m^{2} \,s^{-2} ;$ that of speed $v$ is $m s^{-1}$ and of acceleration $a$ is $m s ^{-2} .$ Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ( $m$ stands for the mass of the body ):
$(a)$ $K=m^{2} v^{3}$
$(b)$ $K=(1 / 2) m v^{2}$
$(c)$ $K=m a$
$(d)$ $K=(3 / 16) m v^{2}$
$(e)$ $K=(1 / 2) m v^{2}+m a$
The $SI$ unit of energy is $J=k g\, m^{2} \,s^{-2} ;$ that of speed $v$ is $m s^{-1}$ and of acceleration $a$ is $m s ^{-2} .$ Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ( $m$ stands for the mass of the body ):
$(a)$ $K=m^{2} v^{3}$
$(b)$ $K=(1 / 2) m v^{2}$
$(c)$ $K=m a$
$(d)$ $K=(3 / 16) m v^{2}$
$(e)$ $K=(1 / 2) m v^{2}+m a$
Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then
Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then
- [IIT 1998]
A force is represented by $\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}$. Where $\mathrm{x}=$ distance and $\mathrm{t}=$ time. The dimensions of $\mathrm{b}^2 / \mathrm{a}$ are :
- [JEE MAIN 2024]