Physics 11th Chap 4 : Topic 1 - Maryam Publications

Physics Chapter 4 : Topic 1

Angles in Radians

1 / 36

One radian is defined as the angle subtended at the center of a circle by an arc whose length is:

A) Equal to the radius

B) Twice the radius

C) Half the radius

D) Equal to the diameter

2 / 36

The SI unit of plane angle is:

A) Arc-second

B) Degree

C) Revolution

D) Radian

3 / 36

A complete revolution corresponds to:

A) $\mathbf{\pi}$ radians

B) $\mathbf{2\pi}$ radians

C) $\mathbf{\pi\ /\ 2}$ radians

D) $\mathbf{4\pi}$ radians

4 / 36

The angle $\mathbf{180}^{\mathbf{o}}$ is equal to:

A) $\mathbf{3\pi\ /\ 2}$ $\mathbf{rad}$

B) $\mathbf{\pi\ /\ 2}$ $\mathbf{rad}$

C) $\mathbf{\pi}$ $\mathbf{rad}$

D) $\mathbf{2\pi}$ $\mathbf{rad}$

5 / 36

Which conversion factor is correct?

A) $\mathbf{1}^{\mathbf{o}}\mathbf{=}$ $\frac{\mathbf{\pi}}{\mathbf{180}}\mathbf{rad}$

B) $\mathbf{1}^{\mathbf{o}}\mathbf{=}$ $\frac{\mathbf{180}}{\mathbf{\pi}}\mathbf{rad}$

C) $\mathbf{1}^{\mathbf{o}}\mathbf{= \pi\ rad}$

D) $\mathbf{1}^{\mathbf{o}}\mathbf{= 2\pi\ rad}$

6 / 36

The angle $\mathbf{45}^{\mathbf{o}}$ equals:

A) $\mathbf{\pi\ /\ 4\ rad}$

B) $\mathbf{\pi\ /\ 6\ rad}$

C) $\mathbf{\pi\ /\ 2\ rad}$

D) $\mathbf{\pi\ /\ 3\ rad}$

7 / 36

The angle $\mathbf{90}^{\mathbf{o}}$ expressed in radians is:

A) $\mathbf{2\pi\ rad}$

B) $\frac{\mathbf{\pi}}{\mathbf{4}}$ $\mathbf{rad}$

C) $\frac{\mathbf{\pi}}{\mathbf{2}}$ $\mathbf{rad}$

D) $\mathbf{\pi\ rad}$

8 / 36

The angle $\mathbf{60}^{\mathbf{o}}$ expressed in radians is:

A) $\mathbf{\pi\ /\ 2}$

B) $\mathbf{\pi\ /\ 6}$

C) $\mathbf{2\pi\ /\ 3}$

D) $\mathbf{\pi\ /\ 3}$

9 / 36

Which angle corresponds to $\mathbf{\pi\ /\ 6}$ radians?

A) $\mathbf{45}^{\mathbf{o}}$

B) $\mathbf{30}^{\mathbf{o}}$

C) $\mathbf{60}^{\mathbf{o}}$

D) $\mathbf{15}^{\mathbf{o}}$

10 / 36

The angle $\mathbf{270}^{\mathbf{o}}$ is equivalent to:

A) $\mathbf{2\pi\ rad}$

B) $\frac{\mathbf{\pi}}{\mathbf{2}}$ $\mathbf{rad}$

C) $\frac{\mathbf{3\pi}}{\mathbf{2}}$ $\mathbf{rad}$

D) $\mathbf{\pi\ rad}$

11 / 36

Which angle has a radian measure of $\mathbf{2\pi}$?

A) Half revolution

B) Full revolution

C) Quarter revolution

D) Two revolutions

12 / 36

An angle of $\mathbf{\pi\ /\ 4}$ radians is:

A) $\mathbf{60}^{\mathbf{o}}$

B) $\mathbf{45}^{\mathbf{o}}$

C) $\mathbf{90}^{\mathbf{o}}$

D) $\mathbf{30}^{\mathbf{o}}$

13 / 36

The angle $\mathbf{120}^{\mathbf{o}}$ in radians is:

A) $\mathbf{2\pi\ /\ 3}$

B) $\mathbf{3\pi\ /\ 4}$

C) $\mathbf{\pi\ /\ 2}$

D) $\mathbf{5\pi\ /\ 6}$

14 / 36

The angle $\mathbf{150}^{\mathbf{o}}$ equals:

A) $\mathbf{3\pi\ /\ 4}$

B) $\mathbf{\pi\ /\ 3}$

C) $\mathbf{5\pi\ /\ 6}$

D) $\mathbf{7\pi\ /\ 6}$

15 / 36

Which angle corresponds to $\mathbf{\pi\ /\ 2}$ radians?

A) $\mathbf{90}^{\mathbf{o}}$

B) $\mathbf{60}^{\mathbf{o}}$

C) $\mathbf{45}^{\mathbf{o}}$

D) $\mathbf{180}^{\mathbf{o}}$

16 / 36

The radian measure of $\mathbf{360}^{\mathbf{o}}$ is:

A) $\mathbf{2\pi}$

B) $\mathbf{4\pi}$

C) $\mathbf{3\pi\ /\ 2}$

D) $\mathbf{\pi}$

17 / 36

Which expression correctly converts radians into degrees?

A) Multiply by $\mathbf{360}$.

B) Divide by $\mathbf{\pi}$.

C) Multiply by $\mathbf{180\ /\ \pi}$.

D) Multiply by $\mathbf{\pi\ /\ 180}$.

18 / 36

The angle $\mathbf{300}^{\mathbf{o}}$ expressed in radians is:

A) $\mathbf{7\pi\ /\ 4}$

B) $\mathbf{3\pi\ /\ 5}$

C) $\mathbf{11\pi\ /\ 6}$

D) $\mathbf{5\pi\ /\ 3}$

19 / 36

Which angle corresponds to $\mathbf{2\pi\ /\ 3}$ radians?

A) $\mathbf{90}^{\mathbf{o}}$

B) $\mathbf{180}^{\mathbf{o}}$

C) $\mathbf{150}^{\mathbf{o}}$

D) $\mathbf{120}^{\mathbf{o}}$

20 / 36

The angle $\mathbf{240}^{\mathbf{o}}$ is equal to:

A) $\mathbf{5\pi\ /\ 3}$

B) $\mathbf{3\pi\ /\ 2}$

C) $\mathbf{4\pi\ /\ 3}$

D) $\mathbf{7\pi\ /\ 6}$

21 / 36

An angle subtending an arc length equal to twice the radius has measure:

A) $\mathbf{2\ rad}$

B) $\mathbf{\pi\ rad}$

C) $\mathbf{1\ rad}$

D) $\mathbf{2\pi\ rad}$

22 / 36

The relation between arc length $\mathbf{(}\mathbf{s}\mathbf{)}$, radius $\mathbf{(r}\mathbf{)}$, and angle $\mathbf{(}\mathbf{\theta}\mathbf{)}$ in radians is:

A) $\mathbf{\theta}\mathbf{=}\mathbf{sr}$

B) $\mathbf{\theta}\mathbf{=}\mathbf{s\ /}\mathbf{\ }\mathbf{r}$

C) $\mathbf{\theta}\mathbf{=}\mathbf{r\ /\ s}$

D) $\mathbf{\theta}\mathbf{=}\mathbf{s}^{\mathbf{2}}\mathbf{\ /\ r}$

23 / 36

If an arc length equals $\mathbf{\pi r}$, the subtended angle is:

A) $\mathbf{1\ rad}$

B) $\mathbf{2\pi\ rad}$

C) $\mathbf{\pi\ rad}$

D) $\mathbf{\pi\ /\ 2\ rad}$

24 / 36

An angle of $\mathbf{1}$ radian is approximately:

A) $\mathbf{45}^{\mathbf{o}}$

B) $\mathbf{180}^{\mathbf{o}}$

C) $\mathbf{90}^{\mathbf{o}}$

D) $\mathbf{57.3}^{\mathbf{o}}$

25 / 36

Which statement about radians is correct?

A) Radian is a unit of length.

B) Radian is a unit of force.

C) Radian is a unit of mass.

D) Radian is a dimensionless measure of angle.

26 / 36

The angle $\mathbf{30}^{\mathbf{o}}$ in radians is:

A) $\mathbf{\pi\ /\ 4}$

B) $\mathbf{\pi\ /\ 6}$

C) $\mathbf{\pi\ /\ 3}$

D) $\mathbf{\pi\ /\ 2}$

27 / 36

The angle $\mathbf{135}^{\mathbf{o}}$ is equal to:

A) $\mathbf{3\pi\ /\ 4}$

B) $\mathbf{7\pi\ /\ 6}$

C) $\mathbf{2\pi\ /\ 3}$

D) $\mathbf{5\pi\ /\ 6}$

28 / 36

The angle $\mathbf{225}^{\mathbf{o}}$ in radians is:

A) $\mathbf{4\pi\ /\ 3}$

B) $\mathbf{3\pi\ /\ 4}$

C) $\mathbf{7\pi\ /\ 6}$

D) $\mathbf{5\pi\ /\ 4}$

29 / 36

Which angle corresponds to $\mathbf{3\pi\ /\ 2}$ radians?

A) $\mathbf{180}^{\mathbf{o}}$

B) $\mathbf{270}^{\mathbf{o}}$

C) $\mathbf{360}^{\mathbf{o}}$

D) $\mathbf{540}^{\mathbf{o}}$

30 / 36

A semicircle subtends an angle of:

A) $\mathbf{\pi\ rad}$

B) $\mathbf{2\pi\ rad}$

C) $\mathbf{\pi\ /\ 2\ rad}$

D) $\mathbf{3\pi\ /\ 2\ rad}$

31 / 36

A quarter circle subtends an angle of:

A) $\mathbf{\pi\ rad}$

B) $\mathbf{\pi\ /\ 4\ rad}$

C) $\mathbf{\pi\ /\ 3\ rad}$

D) $\mathbf{\pi\ /\ 2\ rad}$

32 / 36

If $\mathbf{\theta}\mathbf{= 2}$ radians and radius $\mathbf{= 5\ m}$, the arc length is:

A) $\mathbf{10\ m}$

B) $\mathbf{5\ m}$

C) $\mathbf{2.5\ m}$

D) $\mathbf{7\ m}$

33 / 36

If an arc length is $\mathbf{12\ m}$ and radius is $\mathbf{4\ m}$, the angle in radians is:

A) $\mathbf{6\ rad}$

B) $\mathbf{3\ rad}$

C) $\mathbf{2\ rad}$

D) $\mathbf{4\ rad}$

34 / 36

Which of the following is greater?

A) Cannot be compared

B) $\mathbf{45}^{\mathbf{o}}$

C) $\mathbf{1}$ radian

D) Both equal

35 / 36

Which angle is closest to $\mathbf{1}$ radian?

A) $\mathbf{90}^{\mathbf{o}}$

B) $\mathbf{45}^{\mathbf{o}}$

C) $\mathbf{57}^{\mathbf{o}}$

D) $\mathbf{30}^{\mathbf{o}}$

36 / 36

Why are radians preferred in physics?

A) They eliminate the need for units.

B) They simplify mathematical relationships involving angles, arc length, and circular motion.

C) They are larger than degrees.

D) They are easier to measure directly.

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