The velocity $v$ (in $cm/\sec $) of a particle is given in terms of time $t$ (in sec) by the relation $v = at + \frac{b}{{t + c}}$ ; the dimensions of $a,\,b$ and $c$ are
The velocity $v$ (in $cm/\sec $) of a particle is given in terms of time $t$ (in sec) by the relation $v = at + \frac{b}{{t + c}}$ ; the dimensions of $a,\,b$ and $c$ are
- [AIPMT 2006]
- A
$a = {L^2},\,b = T,\,c = L{T^2}$
- B
$a = L{T^2},\,b = LT,\,c = L$
- C
$a = L{T^{ - 2}},b = L,\,c = T$
- D
$a = L,\,b = LT,\,c = {T^2}$
Similar Questions
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]
Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be
Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be
- [JEE MAIN 2017]
If velocity $[V],$ time $[T]$ and force $[F]$ are chosen as the base quantities, the dimensions of the mass will be
If velocity $[V],$ time $[T]$ and force $[F]$ are chosen as the base quantities, the dimensions of the mass will be
- [JEE MAIN 2021]
Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$, mass of the bob $(m)$ and acceleration due to gravity $(g)$. Derive the expression for its time period using method of dimensions.
Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$, mass of the bob $(m)$ and acceleration due to gravity $(g)$. Derive the expression for its time period using method of dimensions.