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The above equation consisting of basic constants of atomic physics and the gravitational constant G has the dimension of time. e = charge of Electron =  = absolute permittivity =   = Mass of the Proton =  = Mass of the Electron = c = Speed of light in vacuum = G = Universal Gravitational constant = Considering T as the age of the universe and putting the values of the constants, we...
From examples 2.3 and 2.4, we have, Diameter of the Earth = Distance between the Moon and the Earth, = Distance between the Sun and the Earth,  = Diameter of the Sun,  = Let, Diameter of the Moon be     Now, During Solar eclipse, the angle subtended by Sun's diameter on Earth = angle subtended by moon's diameter                 Therefore, the diameter of the moon =
Let the distance of a quasar from Earth be D km. We know , Speed of light =  And, time taken by light to reach us , t = 3.0 billion years =   D =Speed of Light x t        =         =
Given, 77.0 s is the total time between the generation of a probe wave and the reception of its echo after reflection.  Time taken by sound to reach the enemy submarine = Half of the total time =  The distance of enemy ship = Speed of sound x Time taken to reach the submarine =
2.56 s is the total time taken by the LASER to reach Moon and again back Earth.  Time taken by LASER to reach Moon =  We know, Speed of light   The radius of the lunar orbit around the Earth = distance between Earth and Moon =  = Speed of light x Time taken by laser one-way =
The equation for the radius of the nucleus is given by, The volume of the nucleus using the above relation, We know, Mass = Mass number× Mass of single Nucleus = (given)  Nuclear mass Density = Mass of nucleus/ Volume of nucleus =    The derived density formula contains only one variable, and is independent of mass number A. Since  is constant, hence nuclear mass density is nearly constant...
Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: Are the two densities of the same order of magnitude? If so, why? Given, Diameter of sodium = 2.5  Radius, r =   Now, Volume occupied by each atom   We know, One...
In terms of seconds, 100 years =  Given, Difference between the two clocks after 100 years = 0.02 s  In 1 s,  the time difference      Accuracy in measuring a time interval of 1 s =   Accuracy of 1 part in
The derived formula  is dimensionally incorrect. We know, Trigonometric functions are dimensionless.  Hence , [ ] =  and [v] = .  To make it dimensionally correct, we can divide v by (where  is the speed of rain) Thus, L.H.S and R.H.S are both dimensionless and hence dimensionally satisfied. The new formula is :
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