$\mathrm{m}=\mathrm{kc}^{\mathrm{P}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ $\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^0=\left[\mathrm{LT}^{-1}\right]

$\mathrm{m}=\mathrm{kc}^{\mathrm{P}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ $\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^0=\left[\mathrm{LT}^{-1}\right]^{\mathrm{P}}\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]^{-1 / 2}\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]^{1 / 2}$ $\text { By comparing } P=1 / 2$

1.Units, Dimensions and MeasurementDifficult

If mass is written as $\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $\mathrm{k}$ a dimensionless constant)

[JEE MAIN 2024]

A
$1 / 2$
B
$1 / 3$
C
$2$
D
$-1 / 3$

Std 11
Physics

A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is

Medium

View Solution

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is

Medium

View Solution

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

Easy

View Solution

Match List$-I$ with List$-II.$

List$-I$ List$-II$

$(a)$ Magnetic Induction $(i)$ ${ML}^{2} {T}^{-2} {A}^{-1}$

$(b)$ Magnetic Flux $(ii)$ ${M}^{0} {L}^{-1} {A}$

$(c)$ Magnetic Permeability $(iii)$ ${MT}^{-2} {A}^{-1}$

$(d)$ Magnetization $(iv)$ ${MLT}^{-2} {A}^{-2}$

Choose the most appropriate answer from the options given below:

Medium

[JEE MAIN 2021]

View Solution

If force $F$ , velocity $V$ and time $T$ are taken as fundamental units then dimension of force in the pressure is

Medium

View Solution

List$-I$	List$-II$
$(a)$ Magnetic Induction	$(i)$ ${ML}^{2} {T}^{-2} {A}^{-1}$
$(b)$ Magnetic Flux	$(ii)$ ${M}^{0} {L}^{-1} {A}$
$(c)$ Magnetic Permeability	$(iii)$ ${MT}^{-2} {A}^{-1}$
$(d)$ Magnetization	$(iv)$ ${MLT}^{-2} {A}^{-2}$

If mass is written as $\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $\mathrm{k}$ a dimensionless constant)

Similar Questions

A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is

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

If force $F$ , velocity $V$ and time $T$ are taken as fundamental units then dimension of force in the pressure is