Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following
Consider the following equation of Bernouilli’s theorem. $P + \frac{1}{2}\rho {V^2} + \rho gh = K$ (constant)The dimensions of $K/P$ are same as that of which of the following
- A
Thrust
- B
Pressure
- C
Angle
- D
Viscosity
Similar Questions
Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$, where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are
Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$, where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are
- [KVPY 2017]
If the present units of length. time and mass $(m, s, k g)$ are changed to $100\; m, 100\; s$. $\frac{1}{10} \;k g$ then
Match List $-I$ with List $-II$
List $-I$
List $-II$
$A$.
Coefficient of Viscosity
$I$.
$[M L^2T^{–2}]$
$B$.
Surface Tension
$II$.
$[M L^2T^{–1}]$
$C$.
Angular momentum
$III$.
$[M L^{-1}T^{–1}]$
$D$.
Rotational Kinetic energy
$IV$.
$[M L^0T^{–2}]$
| List $-I$ | List $-II$ | ||
| $A$. | Coefficient of Viscosity | $I$. | $[M L^2T^{–2}]$ |
| $B$. | Surface Tension | $II$. | $[M L^2T^{–1}]$ |
| $C$. | Angular momentum | $III$. | $[M L^{-1}T^{–1}]$ |
| $D$. | Rotational Kinetic energy | $IV$. | $[M L^0T^{–2}]$ |
- [JEE MAIN 2024]
The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A\,cos\,Bx + C\,sin\,Dt.$ The dimensional formulae of $D/B$ is
Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)
$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$
Planck's constant $h$, speed of light $c$ and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are)
$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$
- [IIT 2015]