ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Work, Energy, Circular and Rotational Motion (Set 5): 30 multiple-choice questions (40 minutes) with instant scoring and a full…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. A uniform chain 4 m long with mass 2 kg per metre lies on a smooth table with exactly half of it hanging over the edge (g = 10 m s⁻²). The work needed to pull the hanging half slowly back onto the table is:
Answer: A. 40 J
Explanation: The hanging half has mass 4 kg and its centre of mass is 1 m below the table. W = mgh = 4 × 10 × 1 = 40 J.
Q2. A pump lifts 600 kg of water each minute from a well 20 m deep (g = 10 m s⁻²). If the pump is 80 % efficient, the power it draws is:
Answer: A. 2500 W
Explanation: Useful power = mgh/t = 600×10×20/60 = 2000 W. Input = 2000/0.8 = 2500 W.
Q3. A car's engine delivers 40 kW to the wheels. The total resistive force on the car is a constant 1000 N. The maximum speed on a level road is:
Answer: C. 40 m s⁻¹
Explanation: At maximum speed the driving force equals the resistance: P = F v, so v = 40 000/1000 = 40 m/s.
Q4. A 1000 kg car, facing a constant resistive force of 500 N, is accelerating at 1 m s⁻² when its speed is 20 m s⁻¹. The power developed by its engine at that instant is:
Answer: B. 30 kW
Explanation: Driving force F = ma + R = 1000 + 500 = 1500 N. P = Fv = 1500 × 20 = 30 000 W = 30 kW.
Q5. A bullet moving at speed v is brought to rest after penetrating 6 cm into a wooden block with a constant resistive force. A plank of the same wood is fired at by an identical bullet at the same speed. For the bullet to emerge with half its initial speed, the plank's thickness must be:
Answer: B. 4.5 cm
Explanation: Work done is proportional to distance. Losing KE from ½mv² to ¼ of it removes 3/4 of the KE, so the distance is 3/4 × 6 = 4.5 cm.
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Q6. A 2 kg block is released from rest at the top of a smooth quarter-circular track of radius 1.8 m (g = 10 m s⁻²). The normal force exerted by the track on the block at the bottom is:
Q7. A car travels over the top of a circular hump of radius 40 m (g = 10 m s⁻²). The maximum speed at which its wheels stay in contact with the road at the top is:
Q8. A 0.4 kg bob on a string moves in a horizontal circle as a conical pendulum, the string making an angle θ with the vertical where cosθ = 0.8 (sinθ = 0.6; g = 10 m s⁻²). The net (centripetal) force on the bob is:
Q9. A road bend of radius 50 m is banked so that tanθ = 0.8. The speed at which a car needs no friction at all to negotiate the bend (g = 10 m s⁻²) is:
Q10. A solid sphere of mass 5 kg and radius 0.2 m rotates about a tangent to its surface. Its moment of inertia about this axis is:
Q11. Masses of 2 kg and 3 kg are attached to the ends of a light 1 m rod. The moment of inertia about an axis perpendicular to the rod through its centre of mass is:
Q12. A thin hoop of mass 2 kg rolls without slipping along a level floor with its centre moving at 3 m s⁻¹. Its total kinetic energy is:
Q13. Four bodies of the same mass and radius are released together from rest at the top of a rough incline and roll without slipping: a solid sphere, a solid disc, a thin ring and a hollow thin-walled sphere. The first to reach the bottom is the:
Q14. A cord wrapped around a wheel of radius 0.2 m and moment of inertia 2 kg m² is pulled with a constant tension of 10 N. Starting from rest, the kinetic energy of the wheel after 5 s is:
Q15. A disc of moment of inertia 0.4 kg m² spins freely at 10 rad s⁻¹. A lump of putty with moment of inertia 0.1 kg m² about the axis sticks on to it and they spin together. The kinetic energy lost in the process is:
Q16. A flywheel rotating at 120 r.p.m. is brought to rest with uniform angular deceleration in 20 s. The number of revolutions it makes while stopping is:
Q17. A point on the rim of a wheel of radius 0.5 m is at rest at t = 0, and the wheel then speeds up with constant angular acceleration 4 rad s⁻². At t = 0.5 s, the magnitude of the point's total acceleration is:
Q18. The escape speed from Earth's surface is 11 km s⁻¹. A planet has 1/8 of Earth's mass and 1/2 of its radius. The escape speed from its surface is:
Q19. Take Earth's radius R = 6.4 × 10⁶ m and g = 10 m s⁻² at its surface. The extra energy needed to move a 100 kg satellite from a circular orbit of radius 2R to a circular orbit of radius 4R is:
Q20. Which of the following satellites could be geostationary as seen from Lahore (latitude about 31° N)?
Q21. The International Space Station orbits 400 km above Earth's surface. Taking Earth's radius as 6400 km and g = 10 m s⁻² at the surface, the gravitational field strength at the station is approximately:
Q22. A 20 kg crate at rest is pushed along a rough horizontal floor by a constant 100 N horizontal force over 5 m. The friction force is 50 N. The crate's final speed is:
Q23. Which statement correctly describes a conservative force?
Q24. A hydroelectric station receives water of density 1000 kg m⁻³ at 20 m³ s⁻¹ through a vertical drop of 50 m (g = 10 m s⁻²) and delivers 7.5 MW of electrical power. Its overall efficiency is:
Q25. Using 1 kW h = 3.6 × 10⁶ J and g = 10 m s⁻², the mass that 1 kW h of energy can raise through a height of 36 m is:
Q26. A 50 kg crate is dragged at constant speed up a rough 37° incline (sin37° = 0.6, cos37° = 0.8, μ = 0.5, g = 10 m s⁻²) for a distance of 10 m along the slope. The energy dissipated as heat by friction is:
Q27. A 0.5 kg block is pressed against a spring of constant 200 N m⁻¹, compressing it by 0.1 m, and is released on a horizontal surface where μ = 0.2 (g = 10 m s⁻²). Assuming the spring's energy is fully transferred to the block, how far does the block slide before stopping?
Q28. Take Earth's radius R = 6.4 × 10⁶ m and g = 10 m s⁻² at the surface. The gravitational potential energy of a 1 kg mass at a height R above the surface (zero of potential energy at infinity) is:
Q29. A motor delivers a steady torque of 30 N m to a shaft that rotates at 600 r.p.m. The mechanical power delivered is closest to:
Q30. In an amusement-park rotor, riders stand against the inner wall of a vertical cylinder of radius 5 m. The floor drops away and riders stay pinned if μ (wall–rider) = 0.5 (g = 10 m s⁻²). The minimum angular speed of rotation is: