Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energy
Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energy
- A
$ - \frac{5}{6}$
- B
$\frac{1}{2}$
- C
$\frac{1}{3}$
- D
$1$
Similar Questions
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
- [JEE MAIN 2021]
Which is dimensionless
Which is dimensionless
Match List$-I$ with List$-II.$
List$-I$
List$-II$
$(a)$ Torque
$(i)$ ${MLT}^{-1}$
$(b)$ Impulse
$(ii)$ ${MT}^{-2}$
$(c)$ Tension
$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension
$(iv)$ ${MI} {T}^{-2}$
Choose the most appropriate answer from the option given below :
Match List$-I$ with List$-II.$
| List$-I$ | List$-II$ |
| $(a)$ Torque | $(i)$ ${MLT}^{-1}$ |
| $(b)$ Impulse | $(ii)$ ${MT}^{-2}$ |
| $(c)$ Tension | $(iii)$ ${ML}^{2} {T}^{-2}$ |
| $(d)$ Surface Tension | $(iv)$ ${MI} {T}^{-2}$ |
Choose the most appropriate answer from the option given below :
- [JEE MAIN 2021]
Dimensional formula for torque is
Dimensional formula for torque is
- [AIIMS 2002]