In the expression P = E l2m-5 G-2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.
In the expression P = E l2m-5 G-2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.
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1 Answer
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This is a long answer type question as classified in NCERT Exemplar
Dimensions of energy is E= [ML2T-2]
Mass m= [M]
Dimension of E= [ML2T-2]
Dimensions of L= [ML-2T-1]
Dimensions of G= [M-1L3T-2]
By using these values [P]= [ML2T-2] 2 -2
= [M1+2-5+2L2+4-6T-2-2+4]
= [M0L0T0]
After we know that P is dimensionless quantity
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According to question, we can write
Total moles of gas = n = nOxygen + nOxygen =
Volume of gas = 12 × 22.4 litre = 268.8 litre = 2.688 × 105 cm3
Viscosity = Pascal . Second
=
= x = 1, x + 2y = -1, -x + z = 1
y = -1, Z = 0
Viscosity = [P1A-1T0]
1 msD = 1mm
10 vsD = 9msD
1vsD = 0.9 MsD
L.C. = 1MSD – 1VSD = 1 – 0.9 = 0.1 mm
Zero error = 4LC = 0.4 mm
Reading = MSR + VSR + correction
= 4.1 cm + 6 * .01 cm + (-0.04 cm) = (4.1 + 0.06 – 0.04) cm
= 4.12 cm = 412 * 10-2 cm
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