Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G)are three fundamental constants. Which of the following combinations of these has the dimension of length? [2016]

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.
Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length [2016]

1 $\frac{\sqrt{h G}}{c^{3 / 2}}$

2 $\frac{\sqrt{h G}}{c^{5 / 2}}$

3 $\sqrt{\frac{h c}{G}}$

4 $\sqrt{\frac{G c}{h^{3 / 2}}}$

Ans.
(1)

According to question, $l \propto h^{p} c^{q} G^{r}$

$l = k$ $h^{p} c^{q} G^{r}$ ...(i)

Writing dimensions of physical quantities on both sides,

$[M^{0} {LT}^{0}] =$ ${[{ML}^{2} T^{- 1}]}^{p}$ ${[{LT}^{- 1}]}^{^{q}}$ ${[M^{- 1} L^{3} T^{- 2}]}^{r}$

Applying the principle of homogeneity of dimensions, we get

$p - r = 0$ ...(ii), $2 p + q + 3 r = 1$ ...(iii), $- p - q - 2 r = 0$ ...(iv)

Solving eqns. (ii), (iii) and (iv), we get $p = r = \frac{1}{2}, q = - \frac{3}{2}$

From eqn. (i), we get $l = K \frac{\sqrt{h G}}{c^{3 / 2}}$

Solution

Q.
Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length [2016]

1 $\frac{\sqrt{h G}}{c^{3 / 2}}$

2 $\frac{\sqrt{h G}}{c^{5 / 2}}$

3 $\sqrt{\frac{h c}{G}}$

4 $\sqrt{\frac{G c}{h^{3 / 2}}}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length [2016]

1 hGc3/2

2 hGc5/2

3 hcG

4 Gch3/2

Want Us to Email you About Special Offers & Updates?

Q.
Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length [2016]

1 $\frac{\sqrt{h G}}{c^{3 / 2}}$

2 $\frac{\sqrt{h G}}{c^{5 / 2}}$

3 $\sqrt{\frac{h c}{G}}$

4 $\sqrt{\frac{G c}{h^{3 / 2}}}$