I) Explain parallax method for measurement of large distances. Also write range of lengths.
(II) Find the dimensional formula of (I) pressure (II) momentum (III) Work
Answers
Answer:
1.)To measure large distances, such as thedistance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit.
2.) (i)The dimensional formula of pressure is given by,
M1 L-1 T-2
Where,
M = Mass
L = Length
T = Time
Derivation
Pressure (P) = Force × Area-1 . . . . . (1)
Since, Force = Mass × Acceleration
And, acceleration = velocity × time-1= [L T-1] [T]-1 = [L T-2]
∴ The dimensional formula of force = [M] × [L T-2] = Force = M1 L1 T-2 . . . . (2)
The dimensional formula of area = M0 L2 T0 . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Pressure (P) = Force × Area-1
Or, P = [M1 L1 T-2] × [L2]-1 = M1 L-1 T -2.
Therefore, the pressure is dimensionally represented as M1 L-1T -2.
(ii)
The dimensional formula of momentum is given by,
[M1 L1 T-1]
Where,
M = Mass
L = Length
T = Time
Derivation
Momentum (M) = Mass × Velocity . . . . . (1)
The dimensional formula of velocity = [M0 L1 T-1] . . . . (2)
And, the dimensional formula of mass = [M1 L0 T0] . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Momentum = Mass × Velocity
Or, M = [M1 L0 T0] × [M0 L1 T-1] = [M1L1 T-1]
Therefore, momentum is dimensionally represented as [M1L1 T-1].
(iii)Dimensional Formula of Work= (M1L1T-2) x M0L1T0. Dimensional Formula of Work= M1L2T-2. SI units of Work is Joule represented by J. It should be noted that energy of all types ( Surface Tension, Kinetic, Potential etc) have the samedimensional formula as that of Work
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