NEET Class neet Answered

Units of Planck's constant = J s = N m  s  = kg m s^-2 m s = kg m² s^-1

Dimensions of Planck's constant = M L² T^-1

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Units of gravitational constant  = N m² kg^-2  = kg m s^-2  m² kg^-2 = kg^-1 m³ s^-2 

Dimension of gravitational constant = M^-1 L³ T^-2

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Units of speed = m/s^-1

Dimension of speed = L T^-1

If the combination of planck's constant , gravitational constant and speed of light gives length , then

[ M L² T^-1 ]^a  [ M^-1 L³ T^-2 ]^b  [ L T^-1  ]^c  = L

By equating the exponents on both sides, we get

a - b = 0   or  a = b

2 a + 3b + c = 1  or  5a + c = 1  ....................(1)

-a -2b -c = 0 or  3a+c = 0 .....................(2)

by solving eqn.(1) and  (2) , we get

a = 1/2  and  c = -3/2

Hence b = 1/2

hence we get

Hence the combination  ( h^1/2 G^1/2 c^-3/2 ) gives unit of length