33 Years NEET-AIPMT Chapterwise Solutions - Physics 2020

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110 NEET-AIPMT Chapterwise Topicwise Solutions Physics
ANSWER KEY
1. (c) 2. (d) 3. (c) 4. (c) 5. (c) 6. (b) 7. (a) 8. (c) 9. (a) 10. (c)
11. (a) 12. (a) 13. (a) 14. (b) 15. (b) 16. (d) 17. (c) 18. (c) 19. (d) 20. (b)
21. (d) 22. (d) 23. (d) 24. (d) 25. (a) 26. (c) 27. (*) 28. (d) 29. (a) 30. (c)
31. (c) 32. (a) 33. (c) 34. (b) 35. (c) 36. (b) 37. (a) 38. (b) 39. (c) 40. (b)
41. (b) 42. (d) 43. (d) 44. (c) 45. (a) 46. (c) 47. (d) 48. (c) 49. (b) 50. (a)
51. (a) 52. (d) 53. (a) 54. (a) 55. (a) 56. (b) 57. (d) 58. (d) 59. (d) 60. (d)
61. (d) 62. (a) 63. (b)
Hints & Explanations
1. (c) : y = A 0 + Asinwt + Bcoswt.
or (y – A 0 ) = Asinwt + Bcoswt
or y′ = Asinwt + Bcoswt
= ⎛ π ⎞
−
⎝
⎜ ω t ⎠
⎟ + ω
2
t
Amplitude= 2 2 π ⎡ π⎤
A + B + 2AB
cos ⎢Q
φ =
2
⎥
⎣ 2⎦
2 2
= A + B
2. (d)
3. (c) : y = sinwt – coswt
=
⎡ 1 1 ⎤
⎢ − ⎥
⎣
⎦
⎛
⎝
⎜ − π ⎞
2 sinωt cosωt 2 sin ωt
⎠
⎟
2 2
4
It represents a SHM with time period, T = 2π ω .
y= sin 3 ω t = 1 [ sin t − sin t]
4 3 ω 3ω
It represents a periodic motion with time period T = 2π
ω
but not SHM.
⎛ 3π
⎞ ⎛ 3π
⎞
y= 5cos
− t
⎝
⎜ 3ω ⎠
⎟ = 5cos
−
4
⎝
⎜3ωt
⎠
⎟
4
[ Q cos( − θ) = cos θ]
It represents a SHM with time period, T = 2 π
3ω .
y = 1 + wt + w 2 t 2
It represents a non-periodic motion. Also it is not
physically acceptable as y → ∞ as t → ∞.
4. (c) :
The time taken by the particle to travel from
A T
x= 0 to x=
is
2 12
The time taken by the particle to travel from
A T
x= A to x = is
2 6
T T T
Time difference = + =
6 6 3
2π
Phasedifference, φ = × Timedifference
T
2π
T 2π
= × =
T 3 3
2 ⎛1−
cos2ω t ⎞ a acos2ωt
5. (c) : x= asin
ωt = a
⎝
⎜
⎠
⎟ = −
2 2 2
(Q cos2q = 1 – 2sin 2 q)
dx 2ωasin2ωt
∴ Velocity, v = = = ωasin2ωt
dt 2
dv 2
Acceleration, a = =2ω
acos2ωt
dt
For the given displacement x = asin 2 wt,
a ∝ – x is not satisfied.
Hence, the motion of the particle is non simple harmonic
motion.
The given motion is a periodic motion with a time period
2π
π
T = =
2ω
ω
6. (b) : x(t) = asinwt (from the equilibrium position)
At x(t) = a/2
a
a t
2 = sin( ω ) ⇒ sin ⎛ ⎞
⎝
⎜
π 6 ⎠
⎟
π 2πt
= sin( ωt)
or, =
6 T
or t = T/12
7. (a)
8. (c) : x = a sinwt
y = asin(wt + p/2) = acoswt
x 2 + y 2 = a 2
It is an equation of a circle.
9. (a) : For S.H.M., x = ⎛ 2π
Asin
⎝
⎜
T t ⎞
⎠
⎟
when x = A A = ⎛
A
⎝
⎜
T t ⎞
, sin 2π
⎠
⎟
⎛ 2π ⎞
∴ ⋅
⎝
⎜
⎠
⎟ = ⇒ ⎛ 2π ⎝
⎜ ⋅ ⎞
⎠
⎟ = ⎛ π ⎞
sin 1 sin sin
T t T t ⎝
⎜
2 ⎠
⎟
⇒ t = (T/4)