The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be
The frequency of vibration of string is given by $\nu = \frac{p}{{2l}}{\left[ {\frac{F}{m}} \right]^{1/2}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be
- A
$[{M^0}L{T^{ - 1}}]$
- B
$[M{L^0}{T^{ - 1}}]$
- C
$[M{L^{ - 1}}{T^0}]$
- D
$[{M^0}{L^0}{T^0}]$
Similar Questions
The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R = \frac{{\rho l}}{a}$ where $\rho$ is the electrical resistivity. What is the dimensional formula for electrical conductivity $\sigma $ which is reciprocal of resistivity?
- [AIEEE 2012]
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]
Pressure exerted by a gas is found to be $50\, N/m^2$ , then the value of pressure in $CGS$ system is
To find the distance $d$ over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog, intensity (power/area) $S$ of the light from the signal and its frequency $f$. The engineer find that $d$ is proportional to $S ^{1 / n}$. The value of $n$ is:
To find the distance $d$ over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog, intensity (power/area) $S$ of the light from the signal and its frequency $f$. The engineer find that $d$ is proportional to $S ^{1 / n}$. The value of $n$ is:
- [IIT 2014]
If velocity $v$, acceleration $A$ and force $F$ are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of $v,\,A$ and $F$ would be
If velocity $v$, acceleration $A$ and force $F$ are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of $v,\,A$ and $F$ would be