Untitled Document

Question Bank No: 1

1. A pendulum clock is placed on the moon, wher object weighs only one sixth as much as on earth, how many seconds the clock tick out in an actual time of 1 minute the clock keeps good time on earth.

a)		12.25
b)		24.5
c)		2.45
d)		0.245

2. A particle of mass 1 kg is moving in SHM with an amplitude 0.02 and a frequency of 60HZ. The maximum force acting on the particle is

a)		144 $π^{2}$
b)		188 $π^{2}$
c)		288 $π^{2}$
d)		none of the above

3. A simple pendulum has time period given by T = 2 $π \sqrt{l / g .}$ If it is falling down with its support with acceleration a its new period $T^{1}$ is

a)		$T^{1} = 2 π \sqrt{l / g}$
b)		$T^{1} = 2 π \sqrt{l (g - 9)}$
c)		$T^{1} = 2 π \sqrt{l (g + 9)}$
d)		It will not oscillate at all

4. When the displacement is half of the amplitude then what fraction of total energy of a SHM oscillator is kinetic?

a)		2/7 th
b)		3/4th
c)		2/9th
d)		5/7th

5. The potential energy of a particle executing SHM is 2.5J when its displacement is half of amplitude. The total energy of the particle is

a)		2.5 J
b)		10J
c)		12J
d)		18J

6. The vertical extension in a tight spring by a weight of 1 kg suspended from the wire is 9.8cm. The period of oscillation is

a)		20 $π \sec$
b)		2 $π \sec$
c)		2 $π / 10 \sec$
d)		200 $π \sec$

7. Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase when they superimpose, the resultant form of vibration will be

a)		straight line
b)		a parabola
c)		a circle
d)		an ellipsoid

8. The displacement of a particle executing SHM is given by y=0.25 Sin 200 t cm. The maximum speed of the particle is

a)		200 cm/s
b)		100 cm/s
c)		50 cm/s
d)		5.25 cm/s

9. A small mass executes linear SHM about a point O with amplitude r and period T. Its displacement from O at time $\frac{T}{8}$ after passing through O is

a)		$\frac{r}{\sqrt{2}}$
b)		$\frac{r}{2 \sqrt{2}}$
c)		$\frac{r}{2}$
d)		$\frac{r}{g}$

10. A particle of mass 1kg is moving in SHM with path length 0.02 m and a frequency of 50HZ. The maximum force in newton acting on the particle is

a)		15r $π^{2}$
b)		200 $π^{2}$
c)		100 $π^{2}$
d)		50 $π^{2}$

11. A simple pendulem performs S.H.M about x = 0 with an amplitude a and time period T. The speed of pendulum at x = $\frac{a}{2}$ will be

a)		$π \frac{a \sqrt{3}}{T}$
b)		$\frac{π a \sqrt{3}}{2 T}$
c)		$\frac{π a}{T}$
d)		$\frac{3 π^{2} a}{T}$

12. Two springs of constants $K_{1} and K_{2} have equal highest velocities when executing SHM . Then the ratio of their amplitudes given their masses are equal will be$

a)		$K_{1} / K_{2}$
b)		${(K}_{1} / K_{2})^{1 / 2}$
c)		$K_{2} / K_{1}$
d)		( $K_{2} / K_{1})^{1 / 2}$

13. The total energy of simple harmonic motion is E. What will be the kinetic energy of the particle when displacement is half of the amplitude?

a)		3E/4
b)		E/2
c)		E/4
d)		E/3

14. The amplitude of a damped oscillator becomes one half in one minute. The amplitude after 3 minutes will be $\frac{1}{n} times the original, where n is$

a)		2 $\times 3$
b)		$2^{3}$
c)		$3^{2}$
d)		3 $\times 2^{2}$

15. A block of mass m, attached to a spring of spring constant K, oscillate on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed v, when the spring is at its natural length. Before coming to an instantaneous rest, if the block moves a distance x from the mean position. then

a)		x=v $\sqrt{\frac{m}{k}}$
b)		x= $\frac{1}{v} \sqrt{\frac{m}{k}}$
c)		x= $\sqrt{\frac{m}{k}}$
d)		x= $\sqrt{\frac{mv}{k}}$

16. A linear oscillator of force constant 2 $\times 10^{6} {Nm}^{- 1} and amplitude 0.01 m has atotal mechanical energy of 160 J . its$

a)		maximum P.E. is 260J
b)		maximum P.E is 100J
c)		maximum K.E. is 100J
d)		minimum P.E. is zero

17. A spring having a spring constant K is loaded with a mass 'm'. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is

a)		9K
b)		2K
c)		K/2
d)		$K^{2}$

18. A particle with restoring force proportional to displacement and restoring force proportional to velocity is subjected to a force F sin $ω t . If the amplitude is maximum for ω = ω_{1} and the energy of the particle is maximum for ω = ω_{2}$

a)		$ω_{1} = ω_{0} and ω_{2} = ω_{0}$
b)		$ω_{1} = ω_{0}$ and $ω_{2} \neq ω_{0}$
c)		$ω_{1} \neq ω_{0} and ω_{2} = ω_{0}$
d)		$ω_{1} \neq ω_{0}$ and $ω_{2} \neq ω_{0}$

19. For a particle executing S.H.M which of the following statement is not correct?

a)		Total energy of the particle always remains the same
b)		Restoring force is always directed towards a fixed point
c)		Restoring force is maximum at the extreme position
d)		Acceleration of the particle is maximum at the equilibrium position

20. A mass m is vertically suspended from a spring of negligible mass. The system oscillates with a frequency V. What will be the frequency of the system if a mass 4m is suspended from the same spring?

a)		4v
b)		2v
c)		$\frac{v}{2}$
d)		$\frac{v}{4}$

21. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.170s. The frequency of the wave is

a)		1.47 Hz
b)		0.36Hz
c)		0.73Hz
d)		2.94Hz

22. A particle of mass 10g is executing S.H.M. with an amplitude of 0.5m and periodic time ( $π / 5) seconds . The maximum value of the force acting on the particle is$

a)		25N
b)		5N
c)		2.5
d)		0.5N

23. The force constant of a weightless spring is 16N $m^{- 1} . A body of mass 1.0 kg suspended from it is pulled down through 5 cm and then released . The maximum kinetic energy of the system (spring + body) will be$

a)		16 $\times 10^{- 2} J$
b)		4 $\times 10^{- 2} J$
c)		8 $\times 10^{- 2} J$
d)		2 $\times 10^{- 2} J$

24. The percentage change in the time period of a simple pendulum if its length is increased by 4% is

a)		2%
b)		4%
c)		6%
d)		no change

25. A large horizontal surface moves up and down in S.H.M with an amplitude of 1cm. If a mass of 10Kg(which is placed on the surface) is to remain continuously in contact it, the maximum frequency of S.H.M will be

a)		5Hz
b)		0.5Hz
c)		1.5Hz
d)		10Hz

26. A body is executing S.H.M when its displacement from the mean position is 4 cm and 5cm, the corresponding velocity of the body is 10cm/sec and 8 cm/s. Then the time period of the body is

a)		$\frac{π}{2} \sec$
b)		$π \sec$
c)		$\frac{3 π}{2} \sec$
d)		2 $π \sec$

27. The time period of a body executing S.H.M is 0.05 sec and amplitude of vibration is 4 cm. The maximum velocity of body will be

a)		1.6 $π m / s$
b)		2 $π m / s$
c)		3.1m/s
d)		4 $π$ m/s

28. When a particle oscillates simple harmonically its P.E. varies periodically. If the frequency of oscillation of the particles is n, the frequency of P.e variation is

a)		$\frac{n}{2}$
b)		n
c)		2n
d)		4n

29. The bob of pendulum of length L is pulled aside from its equilibrium position through an angle $θ$ and then released. The bob will then pass through its equilibrium position with a speed v, where v equals

a)		$\sqrt{2 gl (1 + \sin θ)}$
b)		$\sqrt{2 gl (1 + \cos θ)}$
c)		$\sqrt{2 gl (1 - \cos θ)}$
d)		$\sqrt{2 gl (1 - \sin θ)}$

30. A particle has simple harmonic motion.The equation of its motion is
y = 5 sin $(4 t - \frac{π}{6})$ .
Where y is the displacement. If the displacement of the particle is 3 units then its velocity is

a)		16
b)		20
c)		$\frac{5}{6} π$
d)		$\frac{2}{3}$ $π$

31. Average energy in one time period of a simple harmonic oscillator whose amplitude is A, angular velocity $ω$ and mass m is

a)		$\frac{1}{4} m ω^{2} A^{2}$
b)		$\frac{1}{2} m ω^{2} A^{2}$
c)		$m ω^{2} A^{2}$
d)		zero

32. The displacement x of a particle in motion is given in terms of time by
x ( x - 4) = 1 - 5 cos $ω$ t

a)		the particle executes SHM
b)		the particle executes oscillatory motion which is not SHM
c)		the motion of the particle is neither oscillatory nor simple harmonic
d)		the particle is not acted upon by a force when it is at x = y

33. When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, the frequency of the kinetic energy is

a)		n/2
b)		n
c)		2n
d)		4n

34. A clock which keeps correct time ar $20^{o}$ C, is subjected to $40^{o}$ C. If coefficient of linear expansion of the pendulum is 12 $\times$ $10^{- 6}$ per ${}^{o}C$ . How much will it gain or loose in time?

a)		20.6 seconds/day
b)		20 seconds/ day
c)		10.3 seconds/ day
d)		5 seconds/ day

35. A particle starts S.H.M from the mean position as shown in the figure. Its amplitude is a and time period is T. At what displacement, its speed is half of its maximum speed?
oscilaltion-q13

a)		$\frac{\sqrt{3} a}{2}$
b)		$\frac{\sqrt{2} a}{3}$
c)		$\frac{2 a}{\sqrt{3}}$
d)		$\frac{3 a}{\sqrt{2}}$

36. A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period t is given by T = 2 $π \sqrt{\frac{l}{g^{'}}}$ . Where $g^{'}$ is given by

a)		g
b)		g - a
c)		g +a
d)		$\sqrt{g^{2} + a^{2}}$

37. Two simple pendulum of length 0.5 m respectively are given small linear displacement in one direction at the same time. They will again to be in the phase when the pendulum of shorter length has completed oscillations

a)		5
b)		3
c)		2
d)		1

38. An instantanwous displacement of a simple harmonic oscillator is x = A cos $(ω t + \frac{π}{4})$ . Its speed will be maximum at time.

a)		$\frac{2 π}{ω}$
b)		$\frac{π}{ω}$
c)		$\frac{π}{2 ω}$
d)		$\frac{π}{4 ω}$

39. A spring 40 mm long is stretched by the application of a force. If 10N force is required to stretch the spring through 1mm, then work done in stretching the spring through 40 mm is

a)		8 J
b)		23 J
c)		68 J
d)		84 J

40. In a simple pendulum, if K.E. is one fourth of total energy, then displacement (X) is related to amplitude A is

a)		X = 2A
b)		X = A
c)		X = $\frac{\sqrt{3}}{2}$ A
d)		X = $\frac{\sqrt{3}}{4}$ A

41. A body is executing S.H.M of amplitude A. Displacement between maximum K.E. and maximum P.E. position for the particle executing S.H.M is

a)		$\pm \frac{A}{2}$
b)		zero
c)		$\pm A$
d)		$A^{2}$

42. The period of oscillation of a mass m suspended from a spring is 2 seconds. If along with it another mass 2 kg is also suspended the period of oscillation increases by one second. The mass m will be

a)		2.6 kg
b)		2 kg
c)		1.6 kg
d)		1 kg

43. Two springs of spring constants 1500 N $m^{- 1}$ and 3000 N $m^{- 1}$ respectively are stretched with the same force. They will have potential energies in the ration

a)		4 : 1
b)		2 : 1
c)		1 : 4
d)		1 : 2

44. If the period of oscillation of mass m suspended from a spring is 2 s, then the period of mass 4 m will be

a)		1s
b)		2s
c)		3s
d)		4s

45. A pendulum bob has a speed of 3 m $s^{- 1}$ at its lowest position. The pendulum is 0.5m long. The speed of the bob when the length makes an angle of $60^{o}$ to the vertical will be (g = 10 m $s^{- 1})$

a)		$\frac{1}{3}$ m/s
b)		$\frac{1}{2}$ m/s
c)		2 m/s
d)		3 m/s

46. The kinetic energy and potential energy of a particle executing S.H.M. will be equal when displacement (amplitude = a) is

a)		a $\sqrt{2}$
b)		$\frac{a}{2}$
c)		$\frac{a}{\sqrt{2}}$
d)		$\frac{a \sqrt{2}}{3}$

47. If the length of second's pendulam is increased by 2%, how many seconds it will lose per day?

a)		3927 s
b)		3727 s
c)		3427 s
d)		864 s

48. A particle executing SHM has maximum velocity and maximum acceleration equal. Then its period is

a)		$\sqrt{2} π$
b)		$2 π$
c)		$\sqrt{2 π}$
d)		$3 π$

49. A mass 0.2 kg is describing a SHM described by x = 2 sin 5t in the MKS system. The maximum force acting on the particle is

a)		2N
b)		5N
c)		10N
d)		25N

50. A particle executes SHM about x = 0 with amplitude A and time period T. The speed of the pendulum at x = A/2 will be

a)		$π A / T$
b)		$π A \sqrt{3} / 2 T$
c)		$π A \sqrt{3} / T$
d)		${3 π}^{2} A / T$