1. An airplane in straight level flight experiences a lift force $L$ that is proportional to the speed of the plane and is perpendicular to the axis of the wings and as shown in diagram.

On a banked turn at the same speed, the wings make an angle $\theta$ with the horizontal.

Which of the following gives the centripetal force on the airplane?

2. The diagram below shows a tennis ball of mass $m$ striking a wall with an initial velocity, $u$, and rebounding with velocity $v$. A second, softer ball of the same mass strikes the wall with the same speed but rebounds with a slower rebound speed.

Which of the following statements is correct about the magnitudes of the impulse and change in momentum applied to the second ball compared to the first?

3. A spring with spring constant $k$ is extended by a distance $x$.

The uncertainty of $k$ is 2% and that of $x$ is 3%.

What is the uncertainty of the potential energy stored in the spring?

4. The take-off speed of a passenger aircraft is 75.0 ms−1. A plane starts from rest and accelerates at a steady rate of 1.25 ms−2. Which of the following correctly states the minimum duration of taxiing and the minimum length of the runway needed for the takeoff?

5. The graph below shows the variation of the resultant force $F$ acting on a box with time t.

The box starts to move from rest. Which of the following graphs shows the variation of the momentum $p$ of the box with time $t$?

A.			B.
C.			D.

6. A car of mass $m$ and a truck of mass $3m$ travelling in opposite directions collide and stick together. The speeds of the car and the truck just before the crash are $2v$ and $v$ respectively. What is their speed after the collision

7. An electric motor is used to raise a block of mass 18.0 kg vertically to the top of a building at a constant speed of 1.5 m s−1. If the power rating of the motor is 297 W, calculate the efficiency of the motor.

8. A box is pulled up a slope inclined at 30° to the horizontal by a force of F. The angle between the direction of $F$ and the plane of the incline is also 30°.

The box is pulled a distance of d up along the slope. What is the work done by F on the box?

9. A ball is projected in an environment where air resistance can be ignored.

Which graph shows the variation of the resultant force $R$ acting on the ball with the height $h$ of the object?

A.			B.
C.			D.

10. The engine of a racing car provides a forward thrust of $800N$. The average of the total resistive forces acting on the car is $300N$ and the car covers a distance of $1.0km$ in $10s$.

What is the average output power of the engine?

11. A box is pulled by a child with a horizontal force of 5$N$. The box moves a horizontal distance of 4$m$ in a time of 2$s$. The average power delivered by the child to the box is

12. A ball rolls horizontally off the edge of the top of a cliff. It hits the ground at a distance 2.0$m$ from the base of the cliff with a vertical speed of 20 m s−1. What is the height of the cliff?

13. A builder uses a block and tackle pulley system to lift a bundle of materials of mass 15 kg to the top of a building of height 6m in 9s. What is the power delivered to the bundle?

14. A rocket ejects hot gas in space in a direction opposite to its travelling direction. What is correct for the magnitude of the momentum and the kinetic energy of the rocket?

15. An object with a weight $W$ connected to one end of a rod of negligible mass rotates at constant speed in a vertical plane.

When the object is at the top position of the circular path, the tension on the rod is zero. What is the magnitude of tension at the bottom position of the circular path?

16. A car enters a roundabout with a speed $v$. The dotted line shows the path of the car. The road is slightly banked at an angle to the horizontal.

The coefficient of friction between the tires of the car and the road is $\mu$. When $\mu$ decreases, which of the following changes could prevent the car from slipping away on this roundabout?

17. A student throws a ball with an initial velocity in the horizontal direction. Air resistance is negligible. At t=2.0 s, the ball has travelled a distance $x$ in the horizontal direction and a distance $y$ in the vertical direction.

What are the horizontal and vertical distances covered at t=1.0s, in terms of x and $y$?

18. A block of wood is placed on a rough inclined surface. Which of the diagrams below correctly represents the forces acting on the block when it is at rest?

A.			B.
C.			D.

19. A pilot intends to fly a plane from point $A$ to point $B$. Due to strong winds, she points the nose of the plane in the direction shown by the vector $P$. Which of the choices below best represents the direction of the wind encountered by the plane?

A.			B.
C.			D.

20. An object of mass M on a string moves in a circle of radius r at a constant speed.

Which of the following statements is true about the motion of the object:

• I.  The resultant work done on the object is zero.
• II.  The velocity of the object is constant.
• III.  The object is accelerating

21. Which of the following is not a suitable SI unit of energy?

22. A basketball is launched at an angle and undergoes projectile motion. Air resistance is negligible. Which of the following is correct for the direction of its velocity vector and its acceleration vector at the highest point of its trajectory?

23. The diagram below shows a car of mass m descending a slope. The car, initially at rest, covers a distance of $27m$ in 3.0 s.

The magnitude of the acceleration is given by

24. An object moves $9m$ east, then 12m north.

What is the magnitude of the total displacement of this object?

25. The Sankey diagram below shows the energy degraded at different stages of a nuclear power plant.

Which of the following sections corresponds to the stage with the highest energy degradation?