SATHEE: Laws of Motion 5 Question 1

Laws of Motion 5 Question 1

1. Two forces $P$ and $Q$ of magnitude $2 F$ and $3 F$ , respectively are at an angle $θ$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $θ$ is

(a) $60^{\circ}$

(b) $120^{\circ}$

(d) $90^{\circ}$

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Answer:

Correct Answer: 1. (b)

Solution:

Resultant force $F_{r}$ of any two forces $F_{1}$ (i.e. $P$ ) and $F_{2}$ (i.e. $Q$ ) with an angle $θ$ between them can be given by vector addition as

In first case $F_{1} = 2 F$ and $F_{2} = 3 F$

$\begin{array}{ll} \Rightarrow & F_{r}^{2} = 4 F^{2} + 9 F^{2} + 2 \times 2 \times 3 F^{2} \cos θ \\ \Rightarrow & F_{r}^{2} = 13 F^{2} + 12 F^{2} \cos θ \dots (i i) \end{array}$

In second case $F_{1} = 2 F$ and $F_{2} = 6 F$ $(∵$ Force $Q$ gets doubled)

$and F_{r}^{'} = 2 F_{r} (G i v e n)$

By putting these values in Eq. (i), we get

$\begin{aligned} {(2 F_{r})}^{2} & = (2 F)^{2} + (6 F)^{2} + 2 \times 2 \times 6 F^{2} \cos θ \\ \Rightarrow 4 F_{r}^{2} & = 40 F^{2} + 24 F^{2} \cos θ \dots (i i i) \end{aligned}$

From Eq. (ii) and Eq. (iii), we get;

$\begin{aligned} 52 F^{2} + 48 F^{2} \cos θ = 40 F^{2} + 24 F^{2} \cos θ \\ \Rightarrow & 12 + 24 \cos θ = 0 or \cos θ = - 1 / 2 \\ or & θ = 120^{\circ} (∵ \cos 120^{\circ} = - 1 / 2) \end{aligned}$

Laws of Motion 5 Question 1

1. Two forces $P$ and $Q$ of magnitude $2 F$ and $3 F$ , respectively are at an angle $θ$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $θ$ is

Answer:

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Laws of Motion 5 Question 1

1. Two forces P and Q of magnitude 2F and 3F, respectively are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. Two forces $P$ and $Q$ of magnitude $2 F$ and $3 F$ , respectively are at an angle $θ$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $θ$ is