Triangle Law

Q.

The resultant of two forces has a magnitude of $20\text{N}$. If one of the forces is of magnitude $20\sqrt{3}\text{N}$and makes an angle of ${30}^{°}$ with the resultant then, the other force must be of magnitude.

1. $10\sqrt{3}N$

2. $20N$

3. $20\sqrt{3}N$

4. $10N$

Q. If the magnitude of sum of the two vectors is equal to the magnitude of difference of the two vectors, then the angle between these vectors is

1. ${45}^o$
2. $0^o$
3. ${90}^{\circ }$
4. ${180}^o$

Q. Two forces $\overrightarrow{A}$ and $\overrightarrow{B}$ have a resultant ${\overrightarrow{R}}_1$. If the magnitude of $\overrightarrow{B}$ is doubled without changing the angle, the new resultant ${\overrightarrow{R}}_2$ is perpendicular to $\overrightarrow{A}$, then

1. $|{\overrightarrow{R}}_1|=|\overrightarrow{A}|+|\overrightarrow{B}|$
2. $|{\overrightarrow{R}}_1|=|\overrightarrow{A}||\overrightarrow{B}|$
3. $|{\overrightarrow{R}}_1|=|\overrightarrow{A}|$
4. $|{\overrightarrow{R}}_1|=|\overrightarrow{B}|$

Q.

If the angle $\alpha$ between 2 forces of equal magnitude is reduced to $\alpha -\frac{\mathrm{\pi }}{3}$, then the magnitude of their resultant becomes $\sqrt{3}$ times the earlier one. The angle $\alpha$ is

1. $\frac{\mathrm{\pi }}{2}$

2. $\frac{2\mathrm{\pi }}{3}$

3. $\frac{\mathrm{\pi }}{4}$

4. $\frac{4\mathrm{\pi }}{5}$

Q.

Can $3$ unequal vectors add to zero?

Q.

The square of resultant of two equal forces is three times their product. Angle between the forces is

1. $\pi$

2. $\pi /2$

3. $\pi /4$

4. $\pi /3$

Q.

Three forces of magnitude $30,60$ and $\mathrm{P}$ acting at a point are in equilibrium. If the angle between the first two is $60°$, the value of $\mathrm{P}$ is

1. $30\sqrt{7}$

2. $30\sqrt{3}$

3. $20\sqrt{6}$

4. $25\sqrt{2}$

Q. Given that $|\overrightarrow{\text{P}}|=|\overrightarrow{\text{Q}}|=|\overrightarrow{\text{R}}|$. If $\overrightarrow{\text{P}}+\overrightarrow{\text{Q}}=\overrightarrow{\text{R}}$ then the angle between $\overrightarrow{\text{P}}$ and $\overrightarrow{\text{R}}$ is ${\theta }_1$, and if $\overrightarrow{\text{P}}+\overrightarrow{\text{Q}}+\overrightarrow{\text{R}}=0$ then the angle between $\overrightarrow{\text{P}}$ and $\overrightarrow{\text{R}}$ is ${\theta }_2$. Then

1. ${\theta }_2={120}^{\circ }$
2. ${\theta }_1={\theta }_2={60}^{\circ }$
3. $2{\theta }_1={\theta }_2$
4. ${\theta }_1={60}^{\circ }$

Q. When two forces of magnitude $P$ and $Q$ are perpendicular to each other, their resultant is of magnitude $R$. When they are at an angle of ${180}^{\circ }$ to each other their resultant is of magnitude $\frac{R}{\sqrt{2}}$. Find the ratio $\frac{P}{Q}$.

1. $\sqrt{3}\pm 2$
2. $5\pm \sqrt{3}$
3. $3\pm \sqrt{5}$
4. $2\pm \sqrt{3}$

Q. Four vectors each of equal magnitude are given below.

Which of the following statement is correct regarding these vectors ?

1. $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=-(\overrightarrow{\text{C}}+\overrightarrow{\text{D}})$
2. $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=\overrightarrow{\text{C}}-\overrightarrow{\text{D}}$
3. $\overrightarrow{\text{A}}+\overrightarrow{\text{B}}=\overrightarrow{\text{C}}+\overrightarrow{\text{D}}$
4. None of the above

Q. When two forces of magnitude $P$ and $Q$ are perpendicular to each other, their resultant is of magnitude $R$. When they are at an angle of ${180}^{\circ }$ to each other their resultant is of magnitude $\frac{R}{\sqrt{2}}$. Find the ratio $\frac{P}{Q}$.

1. $\sqrt{3}\pm 2$
2. $5\pm \sqrt{3}$
3. $2\pm \sqrt{3}$
4. $3\pm \sqrt{5}$

Q.

Find the value of $\theta :$

$cosec4\theta =\frac{2}{\sqrt{3}}$

Q. Two forces $\overrightarrow{A}=5\text{N}$ and $\overrightarrow{B}=2\text{N}$ makes an angle of ${60}^{\circ }$ with each other. Find the magnitude of resultant force.

1. $10\text{N}$
2. $3\text{N}$
3. $\sqrt{29}\text{N}$
4. $\sqrt{39}\text{N}$

Q. Two forces $\overrightarrow{A}=5\text{N}$ and $\overrightarrow{B}=2\text{N}$ make an angle of ${60}^{\circ }$. Find the angle made by resultant force with $\overrightarrow{A}$.

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${\tan }^{-1}(\frac{\sqrt{3}}{6})$
4. ${\tan }^{-1}(\frac{6}{\sqrt{3}})$

Q.

State the property in x + y = y + x

Q.

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