1. 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?

2. 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?

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

5. Vectors $X$ and $Y$ are in the shown directions.

Which of the following shows the sum of the two vectors?

A.			B.
C.			D.

6. As a truck is brought to rest, the brakes apply a force of 5.1×10^3N. Which answer best describes the magnitude of the change in momentum of the truck if the brakes are applied for 3.0 $s$?

7. Two trucks X and Y are pulling a car out of thick mud along a straight path. The only other horizontal force acting on the car is a drag force opposite to the direction of motion. The diagram shows the direction of the force applied by truck $X$ and the direction of motion of the car.

Which of the following vectors shows the direction of the force applied by truck $Y$?

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

The length of one side of a cube is $10.0\pm 0.2cm$.

What is the ratio

[absolute uncertainty of volume of the rectangular prism]/[absolute uncertainty of volume of one cubeabsolute uncertainty of volume of one cube]​?

9. Which of the following is a vector quantity?

10. 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?

11. 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?

12. Express 0.04758 to 3 significant figures.

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

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

What is the uncertainty of the perimeter of the rectangle?

15. 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?

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

17. A ball is projected with an initial speed of 2ms−1 making an angle of 35o with the horizontal as shown.

Which expression gives the vertical component of the velocity vector?

18. 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?

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?

20. 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 ms^−1 and the angle $\theta$ between the velocity of the boat and the side of the stream?

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

22. Which of the following units is not a unit of power?

23. An apple falls 5 m 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?

24. 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.

25. 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.