Question

Two forces of magnitudes (p+q)and (p-q) make an angle 2ß with one another and their resultant makes an angle a with the bisector of the angle between them. Then the ratio of P/ Q is -
a)tan a/tan ß
b)tan ß/2 tan a
c)tan ß/tan a
d)2 tan ß/ tan a
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Answer 1

Answer:

tan α/tan β

Explanation:

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Answer 2

Given:

Two forces of magnitudes (p + q)and (p - q) make an angle 2ß with one another and their resultant makes an angle 'a' with the bisector of the angle between them.

To Find:

Then the ratio of p/q is ?

Solution:

Let, here OA represent (p + q) vector , OB represent (p-q) vector

and OC represent resultant of these two vectors, so it forms a parallelogram OACB.

In a parallelogram OACB,

$\angle AOB = \beta - a$

$\angle ABO = \beta +a$

In ΔAOB, we have

$\dfrac{OA}{sin(\beta + a)}=\dfrac{AB}{sin(\beta-a)} \\\\\Rightarrow \dfrac{p+q}{sin(\beta+a)}=\dfrac{p-q}{sin(\beta-a)}\\\\\Rightarrow \dfrac{p+q}{p-q}=\dfrac{sin(\beta+a)}{sin(\beta-a)}\\\\\Rightarrow \dfrac{p}{q}=\dfrac{sin(\beta+a)+sin(\beta-a)}{sin(\beta+a)-sin(\beta-a)}\\\\\Rightarrow \dfrac{p}{q}=\dfrac{2sin\beta cos a}{2cos\beta sin a}\\\\\Rightarrow \dfrac{p}{q}=\dfrac{tan\beta}{tan a}$

Hence, option (c) is correct.