1. A rectangle has length L=(2 ± 0.1) cm and width $W=(3\pm 0.2)cm$.

What is the uncertainty of the perimeter of the rectangle?

2. Express 0.04758 to 3 significant figures.

3. A point P is subjected to three simultaneous forces of magnitudes FA>FB>FC. Point P is in equilibrium. Which of the following statements is not always true about the magnitudes of the forces?

I. FA=FB+FC
II. FA≤FB+FC
III. FA>FB−FC

4. The diagram shows a cube of side length 0.010m and a metal sphere of radius $0.5cm$. The image below is not to scale.

If there is a set of these spheres that could be melted down, what is the estimated number of spheres required to construct the cube from the material?

5. Which of the following is an estimate of the order of magnitude of the radius of the Earth?

6. Which of the following is a vector quantity?

7. 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?

8. A rectangular prism is obtained by combining two identical cubes as shown in the figure.

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

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

10. Vector $d$ makes an angle $\theta$ with the horizontal as shown. Its magnitude is $5m$ and the magnitude of its horizontal component dx​ is $3m$.

Which of the following is correct about the magnitude and direction of its vertical component?

11. Which of the following is not a fundamental SI unit?

12. A car moves clockwise in a circular path as shown. The direction of its instantaneous velocity at two different times is shown in the diagram.

Which of the following vectors shows the direction of the change in velocity?

A.			B.
C.			D.

13. A stream flows east with a speed vs​. A boat points due south and moves with a speed vo​ relative to the water.

The ratio vo/vs=1/2​

Which of the following is correct about the magnitude in m s^−1 and the angle $\theta$ between the velocity of the boat and the side of the stream?

14. An object starting from rest travels a distance $d$ after a time $t$. If d=(20 ± 1)m, and the time is measured as t=(2.0 ± 0.4)s. Which of the following gives the correct values of the fractional and absolute uncertainties of acceleration?

15. An apple falls 5m in height from a tree. It rebounds from the ground with a quarter of its striking speed. The apple is in contact with the ground for approximately 0.1 s. What is an estimate of the magnitude of the average net force on the apple when it strikes the ground?

16. Which of the following gives the unit for work in fundamental SI units?

17. A spring of negligible mass and length of lolo​ is attached to a fixed point. When the spring is extended by an external force $F$, the length of the spring increases to $l$. The graph shows how the length of the spring varies with the tension in spring. The tension in the spring is equal to $k\Delta l$, where k is a constant and $\Delta l$ is the extension of the spring.

What are the gradient and y-intercept of the graph?

18. An experiment requires the measurement of the radius $R$ and height $H$ of a cylindrical battery to determine its volume. The uncertainty in R is $\Delta R$ and the uncertainty in $H$ is $\Delta H$.

What is the fractional uncertainty in the volume of the battery?

19. A student is using the equation $pV=nRT$ to solve for $n$ with the following percentage uncertainties in the measurements.

What is the percentage uncertainty in the calculated value of n?

20. The volume of a cylinder is calculated from the product of its base area and height. The measurement of the height has an uncertainty of 5% and the uncertainty of the diameter is 1%. What is the uncertainty of the volume of the cylinder?

21. In finding the area of a circular metal plate, a student measures the radius $R$ of the plate and calculates the area to be $\pm a$, where $a$ is the absolute uncertainty on the area. Which of the following would give the fractional uncertainty on R?

22. A student models the relationship between the velocity v of a moving charge in a magnetic field, and the force F acting on it as $F=kv$, with $k$ being a constant

What are the units for $k$ expressed in fundamental SI units?

23. A car is moving with a kinetic energy of 10^5J.

Estimate the order of magnitude of its momemtum.

24. A body moves a distance of 1.5$km$ in 10$ks$.

Which of the following gives the correct magnitudes of both of distance and time?

25. How many significant figures are there in 0.000017000?