The time dependence of a physical quantity P is given by P-P0 e- t2- where - is a constant and t is time- The constant -

The correct option is D Has dimensions of T^ 2 Given, #160; P=P_0 e_α( α t^2) As we know both P and P_0 are pressure so it have the same units ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Dimensional Analysis

The time depe...

Question

The time dependence of a physical quantity $P$ is given by $P = P_{0} e_{α} (- α t^{2})$ , where $α$ is a constant and $t$ is time. The constant $α$

Is a dimension less

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Has dimensions of

P

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Has dimensions of

T^{- 2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Has dimensions of

T

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D Has dimensions of $T^{- 2}$
Given,
$P = P_{0} e_{α} (- α t^{2})$
As we know both P and $P_{0}$ are pressure so it have the same units, therefore $α t^{2}$ must be dimensionless for which
$α = \frac{1}{T^{2}} = T^{- 2}$
So the dimension of $α$ is $[T^{- 2}]$

Suggest Corrections

Similar questions

Q. A physical quantity

P

is given by the relation,

P = P_{0} e^{(- α t^{2})}

. If

t

denotes the time, the dimensions of constant

α

are

Q. The time dependence of physical quantity

P

is found to be of the form

P = P_{o} e^{- α t^{2}}

, where

‘ t^{'}

is the time and

α

is some constant. Then the constant

α

will

Q. The time dependence of a physical quantity

p

is given by

p = p_{0}

exp.

(- α t^{2})

, where

α

is a constant and

t

is the time. The constant

α

Q. The time dependence of a physical quantity

P

is given by

P = P_{0} e^{- α t^{2}}

, where

α

is a constant and t is time. Then constant

α

is / has

Q. The time dependence of a physical quantity

P

is given by

P = P_{0} e x p (- α t^{2})

, where t is time and

α

is a constant and____________

Join BYJU'S Learning Program

The time dependence of a physical quantity P is given by P=P0eα(−αt2), where α is a constant and t is time. The constant α

The correct option is D Has dimensions of T−2Given, P=P0eα(−αt2)As we know both P and P0 are pressure so it have the same units, therefore αt2 must be dimensionless for whichα=1T2=T−2So the dimension of α is [T−2]

The time dependence of a physical quantity $P$ is given by $P = P_{0} e_{α} (- α t^{2})$ , where $α$ is a constant and $t$ is time. The constant $α$

The correct option is D Has dimensions of $T^{- 2}$
Given,
$P = P_{0} e_{α} (- α t^{2})$
As we know both P and $P_{0}$ are pressure so it have the same units, therefore $α t^{2}$ must be dimensionless for which
$α = \frac{1}{T^{2}} = T^{- 2}$
So the dimension of $α$ is $[T^{- 2}]$