A gas bubble from an explosion under water oscillates with a period proportional of $P^a\,d^b\,E^c$ where $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then $a,\,b$ and $c$ are
A gas bubble from an explosion under water oscillates with a period proportional of $P^a\,d^b\,E^c$ where $P$ is the static pressure, $d$ is the density of water and $E$ is the energy of explosion. Then $a,\,b$ and $c$ are
- A
$ - \frac{5}{6},\frac{1}{2},\frac{1}{3}$
- B
$ \frac{1}{2},- \frac{5}{6},\frac{1}{3}$
- C
$\frac{1}{3},\frac{1}{2},- \frac{5}{6}$
- D
$1,\, 1,\, 1$
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 Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................
In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................
- [JEE MAIN 2022]
The dimensions of shear modulus are
The dimensions of shear modulus are
Dimensional formula for thermal conductivity is (here $K$ denotes the temperature)
Dimensional formula for thermal conductivity is (here $K$ denotes the temperature)
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$
A force $F$ is given by $F = at + b{t^2}$, where $t$ is time. What are the dimensions of $a$ and $b$