Q: A measurement of $$3.89\ \mathrm{mm} is to be $$expressed in meters. What is the correct value?

$$3.89 \times 10$$^{-3}$$\ \mathrm{m}$$

Q: Express $$7.62\ \mathrm{kg} in $$micrograms ($$\mu\mathrm{g}).$$

$$7.62 \times 10$$^{9}$$\ \mu\mathrm{g}$$

Q: Rewrite $$0.00016\ \mathrm{kg} in $$scientific notation.

$$1.6 \times 10$$^{-4}$$\ \mathrm{kg}$$

Q: Calculate the dot product $$\vec{A} \cdot \vec{B}$$ for $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 2\hat{j}.$$

$$2 \times 1 + 3 \times 2 = 8$$

Question 1

Which of the following is the correct S.I. unit for force?

Accepted Answer

Newton $$[\mathrm{N}]$$

Question 2

A measurement of $$3.89\ \mathrm{mm} is to be $$expressed in meters. What is the correct value?

Accepted Answer

$$3.89 	imes 10$$^{-3}$$\ \mathrm{m}$$

Question 3

Express $$7.62\ \mathrm{kg} in $$micrograms ($$\mu\mathrm{g}).$$

Accepted Answer

$$7.62 	imes 10$$^{9}$$\ \mu\mathrm{g}$$

Question 4

The earth’s circumference is approximately $$40.1\ \mathrm{Mm} ($$megameters). What is this circumference in kilometers?

Accepted Answer

$$40,100\ \mathrm{km}$$

Question 5

Rewrite $$0.00016\ \mathrm{kg} in $$scientific notation.

Accepted Answer

$$1.6 	imes 10$$^{-4}$$\ \mathrm{kg}$$

Question 6

Convert $$67.5\ \mathrm{mi/hr} to$$ $$\mathrm{m/s}$$ using the conversion $$1\ \mathrm{mi} = 1609\ \mathrm{m}.$$

Accepted Answer

$$30.2\ \mathrm{m/s}$$

Question 7

A wooden cylinder has a radius of $$3.5\ \mathrm{cm}$$ and a height of $$6\ \mathrm{cm}. If $$the mass is $$161\ \mathrm{g}$$, what is the density of the wooden cylinder in $$\mathrm{kg/m^3$}$$?

Accepted Answer

$$697\ \mathrm{kg/m^3$}$$

Question 8

Which of the following equations is dimensionally consistent for calculating distance $$x (in $$meters) for a box moving with initial speed $$v (in$$ $$\mathrm{m/s}$$), acceleration $$a (in$$ $$\mathrm{m/s^2$}$$), and time $$t (in$$ $$\mathrm{s}$$)?

Accepted Answer

$$x = vt + \frac{1}{2}at^2$

Question 9

How many significant figures are in the number $$0.00900$$?

Accepted Answer

3

Question 10

A delivery truck travels $$8$$ miles in the $$+x-$$direction, $$5$$ miles in the $$+y-$$direction, and $$4$$ miles again in the $$+x-$$direction. What is the magnitude (in miles) of its final displacement from the origin?

Accepted Answer

$$\sqrt{(8+4)^2$ + 5^2$} = 13\ \mathrm{miles}$$

Question 11

Given vector $$\vec{A}$$ has components $$A_x = -77\ \mathrm{cm}$$, $$A_y = 36\ \mathrm{cm}$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{(-77)^2$ + 36^2$} = 84.0\ \mathrm{cm}$$

Question 12

Calculate the dot product $$\vec{A} \cdot \vec{B}$$ for $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 2\hat{j}.$$

Accepted Answer

$$2 	imes 1 + 3 	imes 2 = 8$$

Question 13

If two vectors $$\vec{A}$$ and $$\vec{B}$$ have a scalar (dot) product of $$-8$$ and a vector (cross) product of magnitude $$12$$, what is the angle between them?

Accepted Answer

$$\arccos\left(\frac{-8}{|A||B|}\right)$$ and $$\arcsin\left(\frac{12}{|A||B|}\right)$$ both yield $$123.7^\circ$$

Question 14

Which of the following best describes a scalar quantity?

Accepted Answer

A quantity with magnitude only

Question 15

A vector $$\vec{F} is$$ $$65\ \mathrm{m}$$ long, directed $$30.5^\circ$$ below the positive x-axis. What is the y-component $$F_y$$?

Accepted Answer

$$F_y = 65 \sin(-30.5^\circ) = -32.9\ \mathrm{m}$$

Question 16

What is the result of the cross product $$\vec{A} 	imes \vec{B} if$$ $$\vec{A}$$ and $$\vec{B}$$ are parallel?

Accepted Answer

Zero vector

Question 17

Given $$\vec{A} = 4\hat{i} + 3\hat{j}$$ and $$\vec{B} = -2\hat{i} + 3\hat{j}$$, what is the magnitude of $$\vec{C} = \vec{A} 	imes \vec{B}$$?

Accepted Answer

$$18$$

Question 18

Which of the following is the correct unit for the universal gravitational constant $$G in $$Newton’s Law of Gravitation?

Accepted Answer

$$\frac{\mathrm{m}^3}{\mathrm{kg}\cdot\mathrm{s}^2}$$

Units, Physical Quantities, and Vectors – Study Notes

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