Let us consider a system of units in which mass and angular momentum are dimensionless. If length ha

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

easy

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?

$(1)$ The dimension of force is $L ^{-3}$

$(2)$ The dimension of energy is $L ^{-2}$

$(3)$ The dimension of power is $L ^{-5}$

$(4)$ The dimension of linear momentum is $L ^{-1}$

$1,2,4$

$1,2,3$

$1,2$

$1,3$

(IIT-2019)

Solution

Mass $= M ^0 L ^0 T ^0$

$MVr = M ^0 L ^0 T ^0$

$M ^0 \frac{ L ^1}{ T ^1} \cdot L ^1= M ^0 L ^0 T ^0$

$L ^2= T ^1$ $. . . . . . .(1)$

Force $= M ^1 L ^1 T ^{-2} \quad \text { (in SI) }$

$= M ^0 L ^1 L ^{-4}$(In new system from equation $(1)) $

$= L ^{-3}$

Energy $= M ^1 L ^2 T ^{-2} \quad \text { (In SI) }$

$= M ^0 L ^2 L ^{-4}$ (In new system from equation $ (1)) $

$= L ^{-2}$

Power $=\frac{\text { Energy }}{\text { Time }}$

$= M ^1 L ^2 T ^{-5} \quad \text { (in SI) }$

$=M^0 L^2 L^{-6} $ (In new system from equation $(1)) $

$= L ^4$

Linear momentum $= M ^1 L ^1 T ^{-1} \text { (in SI) }$

$=M^0 L^1 L^{-2} $ (In new system from equation $(1)) $

$= L ^{-1}$

Ans. $(1,2,4)$

Standard 11

Physics

If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is

hard

Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

easy

The equation of a circle is given by $x^2+y^2=a^2$, where $a$ is the radius. If the equation is modified to change the origin other than $(0,0)$, then find out the correct dimensions of $A$ and $B$ in a new equation: $(x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2$.The dimensions of $t$ is given as $\left[ T ^{-1}\right]$.

medium

(JEE MAIN-2023)

In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

medium

If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is

medium

Solution

Similar Questions

If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is

Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is

Start a Free Trial Now