chapterwise McQs for practice

(a) 2p[M/2k]^1/2 (b) 2p[2M/k]^1/2 (c) 2p[Mg sin q/2k]^1/2 (d) 2p[2Mg/k]^1/2 6. In damped oscillations, the amplitude of oscillations

is reduced to one-third of its initial value a₀ at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be (a) a₀/2 (b) a₀/6

(c) a₀/9 (d) a₀/4

7. The x-t graph of a particle undergoing SHM is as shown in figure. The acceleration of the particle at t = 4/3 s is

(a) 3

32p cm s^{2 -2} (b) -p^{2 -}₂ 32cm s (c) p² ₂

32cm s^- (d) - 3 -32p cm s^{2 2}

chapterwise McQs for practice

Useful for All National and State Level Medical/Engg. Entrance Exams

8. Two simple harmonic motions are represented by y₁=5

(

_sin2_pt+ 3_cos2_pt y

)

_{, 2}=5_sin(2_{p p}t+ _/4) The ratio of the amplitudes of two SHMs is (a) 1 : 1 (b) 1 : 2

(c) 2 : 1 (d) 1 3:

9. A particle is performing SHM along x-axis with amplitude 6.0 cm and time period 12 s . What is the minimum time taken by the particle to move from x = + 3 cm to x = + 6 cm and back again?

(a) 1 s (b) 2 s

(c) 4 s (d) 6 s

10. Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy be 75% of the total energy?

(a) 112 s (b) 1 6 s (c) 1

4 s (d) 1

3 s

11. Two linear SHMs of equal amplitude A and angular frequencies w and 2w are impressed on a particle along the axes x and y respectively. If the initial phase difference between them is p/2, the resultant path followed by the particle is

(a) y² = x² (1 – x²/A²) (b) y² = 2x² (1 – x²/A²) (c) y² = 4x² (1– x²/A²) (d) y² = 8x² (1 – x²/A²) 12. A particle with restoring force proportional to

displacement and resisting force proportional to velocity is subjected to a force, F = F₀ sin w₀t. If the amplitude of the particle is maximum for w = w₁ and the energy of the particle is maximum for w = w₂ then

(a) w₁ = w₀ and w₂ ≠ w₀ (b) w₁ = w₀ and w₂ = w₀ (c) w₁ ≠ w₀ and w₂ = w₀ (d) w₁ ≠ w₀ and w₂ ≠ w₀

13. A simple pendulum has a length l. The inertial and gravitational masses of the bob are m_i and m_g respectively. Then the time period T is given by

(a) T m l

m g

g

= 2p i

(b) T m l

m g_gⁱ

= 2p

(c) T m m l

g

i g

= × ×

2p

(d) T l

m m_{i g} g

=2p × ×

14. A piece of wood has dimensions a, b and c. Its relative density is d. It is floating in water such that the side c is vertical. It is now pushed down gently and released. The time period is

(a) T abc

=  g





2p  (b) T ba

= dg



 2p 

(c) T g

= dc

 

2p  (d) T dc

=  g



 2p 

15. Which of the following figures represents damped simple harmonic motion?

(a) Time

Displacement

(b) Time

Displacement

(c)

Displacement

Time

(d)

Displacement

Time

Waves

16. Two vibrating tuning forks producing progressive waves given by y₁ = 4sin (500pt) and y₂ = 2sin (506pt) are held near the ear of a person. The person will hear(a) 3 beats/s with intensity ratio between maxima

and minima equal to 2

(b) 3 beats/s with intensity ratio between maxima and minima equal to 9

(c) 6 beats/s with intensity ratio between maxima and minima equal to 2

(d) 6 beats/s with intensity ratio between maxima and minima equal to 9.

17. The transverse displacement y(x, t) of a wave on a string is given by:

y x t e

( )

, = ^-

(

^{ax bt2+ 2+}2 ^abxt

)

. This represents a

(a) standing wave of frequency 1/ b

( )

(b) wave moving in +X direction with speed a b/

( )

(c) wave moving in –X direction with speed b a/

( )

(d) standing wave of frequency b

( )

^.

18. A sonometer wire of length 1.5 m is made of steel.

The tension in it produces an elastic strain of 1%.

What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10³ kg m^–3 and 2.2 × 10¹¹ N m^–2 respectively?

(a) 178.2 Hz (b) 200.5 Hz (c) 770.7 Hz (d) 188.5 Hz

19. The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 0.5 p. The wave velocity is

(a) 144 m s^–1 (b) 384 m s^–1 (c) 256 m s^–1 (d) 720 m s^–1

20. A wire under tension vibrates with a frequency of 450 per second. What would be the fundamental frequency if the wire were half as long, twice as thick and under one fourth tension?

(a) 225 Hz (b) 190 Hz (c) 247 Hz (d) 174 Hz 21. Equation of a stationary wave is

y=10sinp4xcos20pt.

Distance between two consecutive nodes is

(a) 4 (b) 2

(c) 1 (d) 8

22. The speed of sound in hydrogen at NTP is 1270 m s^–1. Then the speed in a mixture of hydrogen and oxygen in the ratio 4 : 1 by volume will be (a) 317 m s^–1 (b) 830 m s^–1

(c) 635 m s^–1 (d) 950 m s^–1

23. An object of specific gravity r is hung from a thin copper wire. The fundamental frequency for transverse standing waves in the wire is 400 Hz. The object is immersed in water so that one third of its volume is submerged. What is the new fundamental frequency?

(a) 200 1 3 r

r

- Hz (b) 400 3 1 3 r r - Hz

(c) 400 1 3 r

r

- Hz (d) 200 3 13 r

r - Hz

24. A closed organ pipe has fundamental frequency 100 Hz. What frequencies (in Hz) will be produced, if its other end is also opened?

(a) 200, 400, 600, 800.. (b) 200, 300, 400, 500...

(c) 100, 300, 500, 700.. (d) 100, 200, 300, 400...

25. A bus is moving with a velocity of 5 m s^–1 towards a huge wall. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air is 335 m s^–1, the number of beats heard per second by the passengers in the bus will be

(a) 3 (b) 4

(c) 5 (d) 6

26. A string is under tension so that its length is increased by 1

n times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

(a) 1 : n (b) n² : 1 (c) n :1 (d) n : 1

27. A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. The speed (v) of wave pulse varies with height (h) from the lower end as shown in

(a)

h v

(b)

h v

(c)

h v

(d)

h v

28. A source of sound gives 5 beats s^–1 when sounded with another source of frequency 100 Hz. The second harmonic of the source together with a source of frequency 205 Hz gives 5 beats s^–1. What is the frequency of the source?

(a) 105 Hz (b) 205 Hz (c) 95 Hz (d) 100 Hz

29. A transverse wave is described by the equation y y=  t x

- 

0sin p u2 l

The maximum particle velocity is equal to four times the wave velocity if

(a) l = py₀/4 (b) l = 2py₀ (c) l = p/y₀ (d) l = py₀/2

30. The equation of a spherical progressive wave is (a) y = a sin wt (b) y = a sin (wt – kr)

The object is not detached from the platform if mg m a m

Kinetic energy of particle of mass m at x axis is K = E – U = a (A⁴ – x⁴)

restoring force on the body is due to springs and not due to gravity pull. Therefore slope is irrelevant.

Here the effective springs constant = k + k = 2k.

Thus time period, T=₂p

[

M k/₂

]

^{1 2/}

6. (c) : a_t = a₀e^–bt, where b = damping coefficient.

If T is the time period of oscillation, then according to the given condition,

At the end of 100 oscillations, a⁰ a e₀ ^{b 100T}

3 = ^{- ×} or 1

3=e^-100bT At the end of 200 oscillations,

a = a₀e^{–b × 200T} = a₀[e^–100bT]²

So time taken in going from x = + 3 cm to x = + 6 cm

12. (c) : Amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped natural vibrations. Velocity resonance takes place (i.e., maximum energy) when frequency of external periodic force is equal to natural frequency of undamped vibrations.

13. (b) : Torque acting on the bob

14. (d) : Let the vertical side of dimension c of block be pushed in liquid when block is floating, then buoyancy force = ab x dw g = ab x g [... dw = 1]

The mass of piece of wood = abcd So, acceleration = –ab x g/abcd = -

  g 

cd x Hence, time period, T dc

= 2p g Amplitude ratio, r A

=A¹=

Comparing it with travelling wave equation y(x, t) = f(x ± vt), v b

= a

Further, +ve sign between x and t shows that the wave travels in the – X direction.

18. (a) : As u= 1 µ = r= r 20. (a) : Frequency of fundamental note

u= 1 µ µ p= r Frequency u becomes 1

2, i.e., 450

2 =225 Hz 21. (a) : Compare the given equation with the standard

equation of a stationary wave

y a x t

Distance between two consecutive nodes

= = =l 2

8

2 4 units

22. (c) : Suppose V is volume of oxygen.

Therefore, volume of hydrogen = 4 V.

Density of mixture,

23. (b) : The fundamental frequency for transverse stationary waves when hung object is in air is

u µ

When the object is immersed one third in water, T′ = Mg – upthrust

New frequency of vibration,

′ = ′ =

(

-

)

\ Number of beats per second u′ - u = 170 – 165 = 5 26. (c)

27. (a) : Let m be the total mass of the rope of length l.

Tension in the rope at a height h from lower end

= weight of rope of length h is

which represents a parabola. Therefore, h versus v graph is a parabola. Option (a) is correct.

28. (a) : Two possible frequencies of source are

= 100 ± 5 = 105 or 95

Frequencies of 2^nd harmonic = 210 or 190

5 beats with source of frequency 205 are possible only when 2^nd harmonic has frequency = 210

\ Frequency of source = 105 Hz

\ Maximum particle velocity =

  dy

dt _max = 2puy₀ × 1 Wave velocity = ul

As 2puy₀ = 4ul, \ l=2p =p 4⁰ 2⁰

y y

30. (d) : The amplitude of a plane progressive wave = a, that of a spherical progressive wave is a/r.

nn

In document Physics for You - January 2016 (Gnv64) (Page 69-74)