Unified Tertiary Matriculation Examination Ā· Physics and Chemistry

Mechanics, Thermal Physics and Waves

35 practice questions, each with the answer and an explanation.

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All 35 questions

  1. A car accelerates uniformly from rest at a constant rate of 2.5 m/sĀ² for 8.0 seconds along a straight highway. What total distance does the vehicle cover during this time?
  2. A stone is projected horizontally with an initial speed of 15 m/s from the edge of a vertical cliff 45 m high. Calculate its horizontal range before striking the ground. (Take g = 10 m/sĀ²)
  3. A block of mass 12 kg rests on a rough horizontal concrete floor. If the coefficient of static friction between the surfaces is 0.35, calculate the minimum horizontal force required to set the block iā€¦
  4. An artillery shell of mass 8.0 kg is fired horizontally at 250 m/s from a mobile gun of mass 1,000 kg on a frictionless track. Determine the recoil velocity of the gun.
  5. A uniform meter rule is balanced horizontally on a knife edge placed at the 40 cm mark when a mass of 60 g is suspended from the 10 cm mark. What is the total mass of the meter rule?
  6. An electric crane lifts a steel beam of mass 500 kg vertically upwards through a height of 24 m in 12 seconds at constant speed. What is the useful mechanical power output of the crane? (Take g = 10 mā€¦
  7. A simple machine has a velocity ratio of 5 and requires an effort of 200 N to raise a load of 800 N. What is the mechanical efficiency of this machine?
  8. A light helical spring extends by 4.0 cm when loaded with a mass of 0.8 kg. Assuming Hooke's law is obeyed, calculate the elastic potential energy stored in the stretched spring. (Take g = 10 m/sĀ²)
  9. A hydraulic press has an input cylinder of cross-sectional area 5.0 cmĀ² and an output piston of area 200 cmĀ². If a force of 40 N is exerted on the smaller piston, what maximum thrust force is generateā€¦
  10. A solid metal cube of side 5.0 cm and density 8.0 g/cmĀ³ is completely submerged in water of density 1.0 g/cmĀ³. Calculate the upthrust experienced by the submerged cube. (Take g = 10 m/sĀ²)
  11. A brass rod has an initial length of 1.50 m at 20Ā°C. Given that the linear expansivity of brass is 1.9 Ɨ 10ā»āµ Kā»Ā¹, calculate its expansion in length when heated to 120Ā°C.
  12. An insulated copper calorimeter contains 0.20 kg of water at 25Ā°C. A piece of hot iron of mass 0.10 kg at 100Ā°C is placed into the water. Assuming no heat loss to surroundings and neglecting calorimetā€¦
  13. Calculate the heat energy required to completely convert 0.05 kg of ice at 0Ā°C into water at 0Ā°C. (Specific latent heat of fusion of ice = 3.36 Ɨ 10āµ J/kg)
  14. A fixed mass of an ideal gas occupies a volume of 2.4 dmĀ³ at a pressure of 100 kPa and temperature 300 K. If the pressure is increased to 150 kPa and volume is reduced to 1.8 dmĀ³, what is its new absoā€¦
  15. Why does a ceramic floor feel substantially colder to bare human feet than a wooden floor at the exact same room temperature?
  16. A sound wave has a frequency of 680 Hz and propagates through ambient air at a speed of 340 m/s. Determine the wavelength of this acoustic wave.
  17. An organ pipe open at both ends has an effective length of 0.85 m. If the speed of sound in air is 340 m/s, calculate the fundamental frequency of acoustic resonance in the pipe.
  18. A light ray traveling in air enters a transparent glass block at an angle of incidence of 45Ā°. If the refractive index of the glass is 1.414 (āˆš2), what is the angle of refraction inside the glass?
  19. Calculate the critical angle for total internal reflection at an optical boundary between glass of refractive index 1.50 and air of refractive index 1.00.
  20. An object is placed 15 cm in front of a convex lens with a focal length of 10 cm. Find the image distance and describe the nature of the formed image.
  21. A simple pendulum has a period of oscillation of 2.0 s at a location where g = 9.8 m/sĀ². What is the approximate length of the pendulum cord?
  22. In a Young double-slit experiment, monochromatic light of wavelength 600 nm illuminates two narrow slits separated by 0.30 mm. If the interference screen is placed 1.5 m away, what is the fringe spaciā€¦
  23. A stationary observer hears a whistle of frequency 500 Hz emitted by an approaching train moving at 20 m/s. Given speed of sound in air is 340 m/s, calculate the observed pitch frequency.
  24. Which optical phenomenon provides direct empirical evidence that light waves are transverse rather than longitudinal?
  25. A flywheel rotates with an initial angular velocity of 10 rad/s and accelerates uniformly at 4.0 rad/sĀ² for 5.0 seconds. What is the total angle turned through by the wheel during this time?
  26. A solid ball of mass 0.5 kg attached to a cord of length 0.8 m rotates in a horizontal circle at a constant speed of 4.0 m/s. Find the centripetal force acting on the ball.
  27. Calculate the gravitational force of attraction between two lead spheres of mass 50 kg and 80 kg whose centers are separated by a distance of 2.0 m. (Universal gravitational constant G = 6.67 Ɨ 10ā»Ā¹Ā¹ā€¦
  28. At what height above the Earth's surface is the acceleration due to gravity reduced to one-fourth of its value at the surface? (Let R be the radius of the Earth)
  29. Two bodies of mass 2.0 kg and 6.0 kg have equal kinetic energies. What is the exact ratio of their linear momenta p1 : p2?
  30. A body executes simple harmonic motion with an amplitude of 0.20 m and a period of 4.0 s. What is the maximum linear speed of the oscillating body?
  31. An ideal heat engine absorbs 2,000 J of thermal energy from a high-temperature heat reservoir and discharges 1,400 J to a cold sink during each cycle. What is its thermal efficiency?
  32. A wire of original length 2.0 m and cross-sectional area 1.0 Ɨ 10ā»ā¶ mĀ² stretches by 1.0 mm under a tension of 100 N. Calculate Young's modulus of elasticity for the wire material.
  33. Water flows through a horizontal pipe of non-uniform cross-section. At a constriction where the pipe narrows and fluid velocity increases, what happens to the internal fluid pressure according to Bernā€¦
  34. A siren produces sound with an intensity of 1.0 Ɨ 10ā»ā“ W/mĀ². What is the sound intensity level in decibels (dB)? (Reference threshold intensity I0 = 1.0 Ɨ 10ā»Ā¹Ā² W/mĀ²)
  35. A projectile is launched from ground level with an initial velocity of 40 m/s at an angle of 30Ā° to the horizontal. Calculate the maximum vertical height reached above ground. (Take g = 10 m/sĀ²)

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