Write the dimensions of $a/b$ in the relation $P = \frac{{a - {t^2}}}{{bx}}$ , where $P$ is pressure, $x$ is the distance and $t$ is the time
Write the dimensions of $a/b$ in the relation $P = \frac{{a - {t^2}}}{{bx}}$ , where $P$ is pressure, $x$ is the distance and $t$ is the time
- A
${M^{ - 1}}{L^0}{T^{ - 2}}$
- B
${M^1}{L^0}{T^{ - 2}}$
- C
${M^1}{L^0}{T^{ 2}}$
- D
${M^1}{L^1}{T^{ - 2}}$
Similar Questions
Of the following quantities, which one has dimensions different from the remaining three
Of the following quantities, which one has dimensions different from the remaining three
- [AIPMT 1989]
The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be
The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be
- [AIIMS 2008]
Which of the following equations is dimensionally incorrect?
Where $t=$ time, $h=$ height, $s=$ surface tension, $\theta=$ angle, $\rho=$ density, $a, r=$ radius, $g=$ acceleration due to gravity, ${v}=$ volume, ${p}=$ pressure, ${W}=$ work done, $\Gamma=$ torque, $\varepsilon=$ permittivity, ${E}=$ electric field, ${J}=$ current density, ${L}=$ length.
Which of the following equations is dimensionally incorrect?
Where $t=$ time, $h=$ height, $s=$ surface tension, $\theta=$ angle, $\rho=$ density, $a, r=$ radius, $g=$ acceleration due to gravity, ${v}=$ volume, ${p}=$ pressure, ${W}=$ work done, $\Gamma=$ torque, $\varepsilon=$ permittivity, ${E}=$ electric field, ${J}=$ current density, ${L}=$ length.
- [JEE MAIN 2021]
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta $. After some time the velocity of the ball attains a constant value known as terminal velocity ${v_T}$. The terminal velocity depends on $(i)$ the mass of the ball $m$, $(ii)$ $\eta $, $(iii)$ $r$ and $(iv)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct
Match List$-I$ with List$-II.$
List$-I$
List$-II$
$(a)$ Capacitance, $C$
$(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$
$(b)$ Permittivity of free space, $\varepsilon_{0}$
$(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$
$(c)$ Permeability of free space, $\mu_{0}$
$(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$
$(d)$ Electric field, $E$
$(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$
Choose the correct answer from the options given below
Match List$-I$ with List$-II.$
| List$-I$ | List$-II$ |
| $(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
Choose the correct answer from the options given below
- [JEE MAIN 2021]