Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful

  • A

    $A/B$

  • B

    $A + B$

  • C

    $A - B$

  • D

    None

Similar Questions

The equation of state of a real gas is given by $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where $\mathrm{P}, \mathrm{V}$ and $\mathrm{T}$ are pressure. volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of :

  • [JEE MAIN 2024]

A book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:

$(a)\;y=a \sin \left(\frac{2 \pi t}{T}\right)$

$(b)\;y=a \sin v t$

$(c)\;y=\left(\frac{a}{T}\right) \sin \frac{t}{a}$

$(d)\;y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$

$(a=$ maximum displacement of the particle, $v=$ speed of the particle. $T=$ time-period of motion). Rule out the wrong formulas on dimensional grounds.

The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are

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]

Match List $I$ with List $II$

LIST$-I$ LIST$-II$
$(A)$  Torque $(I)$    $ML ^{-2} T ^{-2}$
$(B)$   Stress $(II)$   $ML ^2 T ^{-2}$
$(C)$   Pressure of gradient $(III)$   $ML ^{-1} T ^{-1}$
$(D)$   Coefficient of viscosity $(IV)$   $ML ^{-1} T ^{-2}$

Choose the correct answer from the options given below

  • [JEE MAIN 2023]