A physical quantity of the dimensions of length that can be formed out of and is [c is velocity of light, G is the universal constant of gravitation and e is charge] [2017]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^{2}}{4 π ε_{0}}$ is [c is velocity of light, G is the universal constant of gravitation and e is charge] [2017]

1 $c^{2} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

2 $\frac{1}{c^{2}} {[\frac{e^{2}}{G 4 π ε_{0}}]}^{1 / 2}$

3 $\frac{1}{c} G \frac{e^{2}}{4 π ε_{0}}$

4 $\frac{1}{c^{2}} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

Ans.
(4)

Dimensions of $\frac{e^{2}}{4 π ε_{0}} = [F \times d^{2}] = [M L^{3} T^{- 2}]$

Dimensions of $G = [M^{- 1} L^{3} T^{- 2}],$ Dimensions of $c = [L T^{- 1}]$

$l \propto {(\frac{e^{2}}{4 π ε_{0}})}^{p} G^{q} c^{r} ∴ [L^{1}] =$ ${[M L^{3} T^{- 2}]}^{^{p}}$ ${[M^{- 1} L^{3} T^{- 2}]}^{q}$ ${[L T^{- 1}]}^{r}$

On comparing both sides and solving, we get: $p = \frac{1}{2}, q = \frac{1}{2}, and r = - 2 ∴ l \propto \frac{1}{c^{2}} {[\frac{G e^{2}}{4 π ε_{0}}]}^{1 / 2}$

Solution

Q.
A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^{2}}{4 π ε_{0}}$ is [c is velocity of light, G is the universal constant of gravitation and e is charge] [2017]

1 $c^{2} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

2 $\frac{1}{c^{2}} {[\frac{e^{2}}{G 4 π ε_{0}}]}^{1 / 2}$

3 $\frac{1}{c} G \frac{e^{2}}{4 π ε_{0}}$

4 $\frac{1}{c^{2}} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. A physical quantity of the dimensions of length that can be formed out of c,G and e24πε0 is [c is velocity of light, G is the universal constant of gravitation and e is charge] [2017]

1 c2[Ge24πε0]1/2

2 1c2[e2G4πε0]1/2

3 1cGe24πε0

4 1c2[Ge24πε0]1/2

Ans. (4) Dimensions of e24πε0=[F×d2]=[ML3T-2] Dimensions of G=[M-1L3T-2], Dimensions of c=[LT-1] l∝(e24πε0)pGqcr ∴[L1]=[ML3T-2]p[M-1L3T-2]q[LT-1]r On comparing both sides and solving, we get: p=12, q=12, and r=-2 ∴l∝1c2[Ge24πε0]1/2

Want Us to Email you About Special Offers & Updates?

Q.
A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^{2}}{4 π ε_{0}}$ is [c is velocity of light, G is the universal constant of gravitation and e is charge] [2017]

1 $c^{2} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$

2 $\frac{1}{c^{2}} {[\frac{e^{2}}{G 4 π ε_{0}}]}^{1 / 2}$

3 $\frac{1}{c} G \frac{e^{2}}{4 π ε_{0}}$

4 $\frac{1}{c^{2}} {[G \frac{e^{2}}{4 π ε_{0}}]}^{1 / 2}$