Plank 's constant (h) speed of length in...

Plank 's constant (h) speed of length in vacium (C) and newton 's gravitational constant (G) are three fundamental constant .Which of the following combinations of these has the dimension of length?

`sqrt((hc)/(G))`

`sqrt((Gc)/(h^(3//2))`

`(sqrt(hG))/(c^(3//2))`

`(sqrt(hG))/(c^(5//2))`

Text Solution

Verified by Experts

The correct Answer is:

` l prop h^(x) G^(y) c ^(z)`
`M^(0)L^(1)T^(0)= (ML^(2)T^(-1))^(x) (M^(-1)L^(3)T^(-2))^(y)(LT^(-1))^(z)`
`" " = M^(x-y) L ^(2x+3y+z) T^(-x-2y-z)`
Equating :
`{:(x-y=0),(2x+3y+z=1),(-x-2y-z=0):}} rArr x = (1)/(2) , y = (1)/(2), z = - (3)/(2)`
`rArr l prop (sqrt(hG))/(c^(3//2))`

Topper's Solved these Questions

PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT
ALLEN|Exercise EXERCISE-II AIIMS 2016|2 Videos
PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT
ALLEN|Exercise EXERCISE-III|20 Videos
PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT
ALLEN|Exercise EXERCISE-II AIIMS 2015|2 Videos
MISCELLANEOUS
ALLEN|Exercise SUBJECTIVE QUESTION|9 Videos
SEMICONDUCTORS
ALLEN|Exercise Part-3(Exercise-4)|51 Videos

Plannk's constant (h),speed of light in vaccum (c) and Newton's gravitational constant (G) are thse fundamental has the dimension of light?

`sqrt((hc)/(G))`

`sqrt((Gc)/(h^(3//2))`

`(sqrt(hG))/(c^(3//2))`

`sqrt((hG)/(c^(3//2))`

The dimensions of gravitational constant G are :

`[MLT^(-2)]`

`[ML^(3)T^(-2)]`

`[M^(-1)L^(3)T^(-2)]`

`[M^(-1)LT^(-2)]`

If Planck's constant (h) and speed of light in vacuum (c ) are taken as two fundamental quantites, which on of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities ?

Mass of electron `(m_e)`

Universal gravitational constant (G)

charge of electron (e )

Mass of proton `(m_p)`