1. A simple pendulum undergoes simple harmonic motion. The graph shows the variation of a quantity $y$ with horizontal displacement x from the equilibrium position.

Which of the following quantities could be represented by quantity y?

2. An object executes simple harmonic motion with an amplitude of x0​. Which graph shows the relationship between the kinetic energy Ek​ and the displacement $x$ from the equilibrium position of the object?

A.			B.
C.			D.

3. A train is traveling at 30ms^−1 towards a stationary observer. It sounds a horn of frequency $450Hz$.

Which of the following statements is true about the observed frequency compared with the emitted frequency as the train approaches?

4. A boy tied two identical ropes to a fixed wall for a fitness exercise. He shakes the ropes to form waves.

A point on the right rope oscillates with a period of $0.4s$. A point on the left rope oscillates with a period of $0.2s$.

What is the ratio = wavelength of right rope/wavelength of left ?

5. A parallel beam of light passes through two parallel slits and an interference pattern is formed on a distant screen. The fringe separation is too small to measure. Which of the following would increase the fringe separation?

I. Increase the distance between slits and screen
II. Replace the light source with one with a longer wavelength
III. Increase the slit separation

6. A body performs simple harmonic motion (shm). Which of the following could be the speed against the time graph for one period of motion?

A.				B.
C.				D.

7. An object on a horizontal spring performs simple harmonic motion. The position of the object as a function of time is given by x=5 cos⁡(2t).

Which of the following expressions gives the acceleration of this object as a function of time?

8. Monochromatic light falls on a diffraction grating and a diffraction pattern is formed on a screen. A wider beam of light is used so that more slits of the same diffraction grating produce the interference pattern. Which one of the following is correct in terms of intensity and width of primary maxima?

9. Water drips onto a pond every 3.0 seconds. The speed of water waves in the pond has been measured to be 1.2ms^−1. What is the wavelength of water waves generated because of the drops?

10. A spring-mass system executes simple harmonic motion with an amplitude of $20cm$ and maximum elastic potential energy of $100J$. What is the displacement of the mass when the elastic potential energy of the system is $25J$?

11. A beam of parallel light with a wavelength of λ is incident on a narrow slit. A diffraction pattern is formed on a distant screen. The angle of diffraction between the central maximum and the first minimum is θ. What would be the angle of the first diffraction minimum for the light with a wavelength of 3λ?

12. The diagram shows a beam of light passing from medium $X$ to medium $Y$.

If the angle of incidence of the light increases, which of the following changes can be implemented to keep the angle of refraction the same?

I. Medium X can be replaced with another medium which has a lower refractive index.
II. Medium X can be replaced with another medium which has a higher refractive index.
III. Medium Y can be replaced with another medium which has a higher refractive index.

13. An object with a mass of $m$ is connected to a spring on a frictionless horizontal surface.

The object is displaced by $x$ from its equilibrium point O to point $A$ and executes simple harmonic motion with a period of $T$. Which of the following are true if the object is displaced by $2x$?

I. The angular frequency of the oscillation will be less.
II. Total energy of the object will be greater.
III. The average speed of the object will not change.

14. A radio wave of frequency $90MHz$ travels a distance $d$. The number of wavelengths that can fit into this distance is 6000. What is $d$?

15. A mass-spring system executes simple harmonic motion with a period $T$ in a vertical plane. What is the period when the oscillating mass is doubled and the system is brought to a planet where the gravitational field strength at the surface is halved?

16. For a body executing simple harmonic motion, which statement is not possible?

18. A geostationary satellite is used for TV broadcasting. It orbits so that its position remains fixed above a receiver on earth. It undergoes circular motion with a speed of $v$ and the emitted frequency for a channel is $f$. Which of the following is correct?

19. Three monochromatic light sources, $K$, $L$, and $N$, are incident on a single slit separately. The diagram shows obtained diffraction patterns on the screens for each light source along with the relative widths of their central maxima.

In which option are the possible colors of the light sources given correctly?

20. The graph below shows the variation with displacement $x$ of the acceleration $a$ from the equilibrium position of a particle that undergoes simple harmonic motion.

The magnitude of the slope of the graph is directly proportional to

21. A string fixed at both ends oscillates in a standing wave as shown with a wavelength of $400mm$.

What is the length of the string?

22. Two simple pendulums with lengths $16L$ and $9L$ have masses $4M$ and $3M$ respectively. The period of the mass of $M$ is T. What is the period of mass of $3M$?

23. A traveling source produces sound waves nearby a child. The wavefronts of the sound waves and the position of a child are seen in the figure below.

The frequency of the generated sound waves is $f$. Which of the following is correct for both the direction of motion of the source and the observed frequency of the sound waves by the child?

24. Incident light of wavelength $600nm$ is emitted towards two slits separated by $1\mu m$. The interference pattern is observed on a wall. The distance between two adjacent maxima is $1.2m$. What is the distance of the wall from the slits?

25. Sound waves in water travel approximately 4.5 times faster than in air. Which of the following diagrams correctly shows the wavefronts of sound as they pass from air to water?

A.				B.
C.				D.