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# Check that the ratio ke^2/G me.mp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify? - CBSE (Science) Class 12 - Physics

#### Question

Check that the ratio ke2/G memp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

#### Solution

The given ratio is

(ke^2)/(Gm_cm_p)

Where,

G = Gravitational constant

Its unit is N mkg−2.

me and mp = Masses of electron and proton.

Their unit is kg.

e = Electric charge.

Its unit is C.

k=A constant

=1/(4piin_0)

0 = Permittivity of free space

Its unit is N mC−2.

therefore, unit of the given ratio (ke^2)/(Gm_cm_p)=([Nm^2C^-2][c^-2])/([Nm^2kg^-2][kg][kg])=m^0L^0T^0

Hence, the given ratio is dimensionless.

= 1.6 × 10−19 C

G = 6.67 × 10−11 N mkg-2

me= 9.1 × 10−31 kg

mp = 1.66 × 10−27 kg

Hence, the numerical value of the given ratio is

(ke^2)/(Gm_cm_p)=(9xx10^9xx(1.6xx10^-19)^2)/(6.67xx10^-1xx9.1xx10^-3xx1.67xx10^-22)~~2.3xx10^39

This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 1: Electric Charge and Fields
Q: 3 | Page no. 46

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Solution Check that the ratio ke^2/G me.mp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify? Concept: Coulomb’s Law.
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