33 Years NEET-AIPMT Chapterwise Solutions - Physics 2020

Units and Measurements
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7
−
− −
∴ R = [ 2 2
ML T / IT] 2 3 2
= [ ML T I ]
[I]
22. (b) : h 2 −2
E
I
= λ
c × I
= [ ML T ][ L]
−1 2
[ LT ] × [ ML ]
h
I = −1
[ T ] = frequency.
23. (a) : Gravitational constant G
2
force × (distance)
=
mass × mass
−2 2
[MLT ][L ]
\ Dimensions of G = = [M
–1
L 3 T –2 ]
[M][M]
24. (c) : Dimensions of Planck’s constant
2 −2
Energy [ML T ] 2 −1
h = = = [ML T ]
Frequency −1
[T ]
Dimensions of angular momentum L
= Moment of inertia (I) × Angular velocity (w)
= [ML 2 ][T –1 ] = [ML 2 T –1 ]
25. (b) : Dimensions of force = [MLT –2 ]
Dimensions of impulse = [MLT –1 ].
26. (b) : Impulse = Force × Time.
Therefore dimensional formula of impulse
= Dimensional formula of force × Dimensional
formula of time = [MLT –2 ][T] = [MLT –1 ] and
dimensional formula of linear momentum
[p] = [MLT –1 ].
27. (a)
28. (c) : Units of RC = ohm × ohm –1 × second
= second. Therefore dimensions of RC = time.
29. (b) : Pressure = Force
Area
Therefore dimensions of pressure = Force
Area = ML–1 T –2 .
30. (d) : Dimensions of energy E = [ML 2 T –2 ]
Dimensions of volume v = [L 3 ]
Dimensions of force F = [MLT –2 ]
Dimensions of area A = [L 2 ]
Dimensions of voltage V = [ML 2 T –3 A –1 ]
Dimensions of charge q = [AT]
Dimensions of angular momentum L = [ML 2 T –1 ]
\ Dimensions of E 2 − 2
v = [ML T ]
= −1 −2
[ML T ]
3
[L ]
Dimensions of F − 2
A = [MLT ]
= −1 −2
[ML T ]
2
[L ]
Dimensions of Vq 2 −3 −1
v = [ML T A ][AT]
= [ML
3
–1 T –2 ]
[L ]
Dimensions of angular momentum is [ML 2 T –1 ] while
other three has dimensions [ML –1 T –2 ]
31. (c) : Magnetic flux, φ= = ⎛ ⎝ ⎜ F ⎞
BA
⎠
⎟ A
Il
= [ −2 ][ 2
MLT L ] 2 −2 −1
= [ ML T A ].
[ A][L]
32. (a) : Permeability of free space
π
µ 0 = 2 × force × distance
current × current × length
−2
[MLT ][L]
Dimensional formula of µ 0 =
= [MLT –2 A –2 ]
[A][A][L]
33. (d) : Dimensions of force F = [MLT –2 ]
Dimensions of velocity gradient ∆ −1
v
∆Z = [LT ]
= [T –1 ]
[L]
Dimensions of area A = [L 2 ]
∆
Given F = −ηA
v ∆Z
Dimensional formula for coefficient of viscocity
− 2
F [MLT ] −1 −1
η= = = [ ML T ]
⎛ ∆v
⎞ 2 −1
( A)
[L ][T ]
⎝
⎜
∆ ⎠
⎟
Z
34. (c) : Induced emf | ε | =L dI
dt
where L is the self inductance and dI is the rate of change
dt
of current.
\ Dimensional formula of
2 −3 −1
| ε | [ML T A ] 2 −2 −2
L = = = [ ML T A ]
dI
−1
[AT ]
dt
35. (a) : Torque (t) = Force × distance
Dimensional formula for (t) = [MLT –2 ][L]= [ML 2 T –2 ]
Charge
36. (a) : Capacitance C =
Potentialdifference
[AT]
Dimensions of C =
= [M –1 L –2 T 4 A 2 ]
2 −3 −1
[ML T A ]
Potential difference
Resistance R =
Current
= [ML 2 T −3 A −1
] = [ML 2 T –3 A –2 ]
[A]
Dimensional formula of CR
= [M –1 L –2 T 4 A 2 ][ML 2 T –3 A –2 ] = [T]
As the (CR) has dimensions of time and so is called time
constant of CR circuit.
37. (d) : Angular momentum L
= Moment of inertia I × Angular velocity w.
\ Dimensional formula L = [ML 2 ][T –1 ]
= [ML 2 T –1 ]
2
e
38. (d) : Dimensions of
2 3 2
F d
4πε = × = −
[ ] [ ML T ]
0
Dimensions of G = [M –1 L 3 T –2 ],
Dimensions of c = [LT –1 ]
p
e q r
l ∝ ⎛ 2 ⎞
G c
⎝ ⎜ ⎟
4πε 0 ⎠