The force is given in terms of time $t$ and displacement $x$ by the equation
${F}={A} \cos {Bx}+{C} \sin {Dt}$
The dimensional formula of $\frac{{AD}}{{B}}$ is -
The force is given in terms of time $t$ and displacement $x$ by the equation
${F}={A} \cos {Bx}+{C} \sin {Dt}$
The dimensional formula of $\frac{{AD}}{{B}}$ is -
- [JEE MAIN 2021]
- A
$\left[{ML}^{2} {T}^{-3}\right]$
- B
$\left[{M}^{2} L^{2} {T}^{-3}\right]$
- C
$\left[{M}^{1} {L}^{1} {T}^{-2}\right]$
- D
$\left[{M}^{0} {LT}^{-1}\right]$
Similar Questions
Match List $I$ with List $II$ :
List $I$ (Physical Quantity)
List $II$ (Dimensional Formula)
$(A)$ Pressure gradient
$(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$
$(B)$ Energy density
$(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$
$(C)$ Electric Field
$(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$
$(D)$ Latent heat
$(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$
Choose the correct answer from the options given below:
Match List $I$ with List $II$ :
| List $I$ (Physical Quantity) | List $II$ (Dimensional Formula) |
| $(A)$ Pressure gradient | $(I)$ $\left[ M ^0 L ^2 T ^{-2}\right]$ |
| $(B)$ Energy density | $(II)$ $\left[ M ^1 L ^{-1} T ^{-2}\right]$ |
| $(C)$ Electric Field | $(III)$ $\left[ M ^1 L ^{-2} T ^{-2}\right]$ |
| $(D)$ Latent heat | $(IV)$ $\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$ |
Choose the correct answer from the options given below:
- [JEE MAIN 2023]
In $SI\, units$, the dimensions of $\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} $ is
In $SI\, units$, the dimensions of $\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} $ is
- [JEE MAIN 2019]
An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is
An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is
The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
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- [AIPMT 1990]
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
- [JEE MAIN 2019]