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Question Bank No: 2

1. The mass and diameter of a planet are twice those of earth. The period of oscillation of a pendulum on this planet will be (if this is a seconds pendulum on earth)

a)		$1 / \sqrt{2} s$
b)		$\sqrt{2} s$
c)		2s
d)		1/1 s

2. A mass m attached to a spring oscillates with a period of 2s. If the mass is increased by 2kg, the period increases by 1s. The mass m is

a)		0.8 kg
b)		1.6 kg
c)		2.25 kg
d)		1.25 kg

3. A flat horizontal platform moves up and down in SHM with an amplitude $a$ m. A small body is kept on the platform. The maximum frequency (in Hertz) the platform can have if the body is not to seperate from it at any part of the motion is

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

4. The length of a seconds pendulum on the surface of the earth is 1m. The length of the seconds pendulum on the surface on the moon where g is 1/6th the value of g on the surface on the earth is

a)		(1/6) m
b)		1/36 m
c)		36 m
d)		6m

5. A particle executing SHM has an acceleration 0.02 ${ms}^{- 2}$ when its displacement is 0.08m. Its time period is

a)		1s
b)		2s
c)		4 $π$
d)		5s

6. The equation for the displacement of a particle executing SHM is x(t) = 0.6 sin (2 $π$ t + $π$ /3) m. The maximum speed of the particle in ${ms}^{- 1}$ is

a)		1.2 $π$
b)		12 $π$
c)		2 $π$
d)		0.12 $π$

7. A particle executing SHM of amplitude 25 cm and time period 3s. What is the minimum time required for the particle to move between two points 12.5 cm on either side of the mean position?

a)		0.25 s
b)		0.5 s
c)		$π / 6$ s
d)		$π / 3$ s

8. A body executing SHM has period 3.14 s and amplitude 3m. Its velocity at x = 2m is

a)		10 ${ms}^{- 1}$
b)		1 ${ms}^{- 1}$
c)		20 ${ms}^{- 1}$
d)		2 $\sqrt{5} {ms}^{- 1}$

9. The time period of a pendulumin a satellite orbiting the earth is

a)		zero
b)		infinity
c)		1/ $π$
d)		$π$

10. A particle is executing SHM with period 6s and amplitude 3cm. Its maximum speed in ${cms}^{- 1}$

a)		$3 π$
b)		$π$
c)		$π / 2$
d)		$2 π$

11. The equation of SHM with amplitude %m and period 0.5 s is

a)		$y = 5 \sin 4 π t$
b)		$y = 0.5 \sin 2 π t / 5$
c)		$y = 5 \sin π t / 0.5$
d)		$y = 5 \sin 2 π t$

12. A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x = A to x =A/2

a)		T/6
b)		T/4
c)		T/3
d)		T/2

13. The maximum acceleration of a particle executing SHM is ( ${5 π}^{2} / 9$ ) ${cms}^{- 2}$ and the maximum velocity ( $5 π / 3$ ) ${cms}^{- 1}$ .The amplitude is

a)		$15 / π cm$
b)		$π / 3 cm$
c)		4 cm
d)		5 cm

14. A body performing SHM has an acceleration of 8 ${cm / s}^{2}$ when its displacement is 2 cm. The periodic time of oscillation is

a)		6.28 s
b)		3.14 s
c)		0.314 s
d)		0. 623 s

15. The phase difference between velocity and displacement of a particle executing SHM is

a)		0
b)		$π / 2$
c)		$π / 4$
d)		$π / 6$

16. A steel spring has an unstretched length of 8 cm and when a weight is hung from it, its length becomes 14cm. The period of oscillation of the weight is

a)		0.263 s
b)		0.491 s
c)		0.592 s
d)		2s

17. Work done by a simple pendulum during one complete oscillation is

a)		(1/2) k $A^{2}$
b)		1/2 ( $A^{2} - y^{2}$ )
c)		1/2 ${ky}^{2}$
d)		zero

18. A particle moves such that its acceleration 'a' is given by a = -bx; where x is the displacement and b is constant. The period of oscillation is

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

19. A particle is vibrating simple harmonically with an amplitude of 4 cm. What is the displacement of the particle from the equilibrium position when its energy is half potential and half kinetic?

a)		1 cm
b)		$\sqrt{2}$ cm
c)		2 cm
d)		$2 \sqrt{2}$ cm

20. A uniform spring of force constant k is cut into two pieces whose length are in the ratio 1 : 2. What is the force constant of the longer piece of the spring?

a)		k/2
b)		k
c)		3k/2
d)		2k

21. The length of a simple pendulum is increased by 44%. What is the percentage increase in its time period?

a)		10%
b)		20%
c)		40%
d)		44%

22. In the figure $S_{1}$ and $S_{2}$ are two identical springs. The oscillation frequency of the mass is f. If one spring is removed, the frequency will become

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

23. The particle execute SHM with amplitude 0.5cm and frequency 5Hz. The maximum speed of the particle will be

a)		$π$ m/s
b)		0.5 $π$ m/s
c)		5 $π \times 10^{- 5} m / s$
d)		100 $π m / s$

24. The PE of a simple pendulum is maximum when it is

a)		at the equilibrium position
b)		at the turning points of the oscillation
c)		in between the above two cases
d)		PE is same at all points

25. When a certain weight is suspended from a long uniform wire., its length increased by 1 cm. If the same weight is suspended from another wire of same material and length, but having a diameter half the first one, the increase in length will be

a)		0.5 cm
b)		2 cm
c)		4 cm
d)		8 cm

26. The motion of a particle executing S.H.M is giving by x = 0.01 sin $100 π (t + 0.05)$ , where x is in meters and t is in seconds. The time period is

a)		0.01 sec
b)		0.02 sec
c)		0.1 sec
d)		10.2 sec

27. A body travels a circular path. The ratio of the distance to displacement of the particle during half a revolution is

a)		$π$ :2
b)		$π$ :1
c)		2: $π$
d)		1: $π$

28. The numerical ratio of displacement to distance is always

a)		<1
b)		>1
c)		Equal to 1
d)		Equal to or less than 1