Question

9. If x and y components of a force are 2 N and -3N
respectively then express the force in Cartesian form. Find
the magnitude of force and direction of force w.r.to x-axis
​

Answer 1

Explanation:

Fraction – 5⁄12

Question states that a fraction becomes ⅓ when 1 is subtracted from the numerator of the fraction. Similarly, when 8 is added to the denominator of the fraction the fraction becomes ¼. & we've to calculate the fraction.

Let's say, that the Numerator be x and Denominator be y of the fraction.

• C A S E : I

A fraction becomes ⅓ when 1 is subtracted from the numerator of the fraction.

↠⠀⠀ (x – 1)/y = ⅓

↠⠀⠀ 3(x – 1) = y

↠⠀⠀ 3x – 3 = y

↠⠀⠀ 3x – y = 3 ⠀⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀ —eqₙ ( i )

• C A S E : I I

A fraction becomes ¼ when 8 is added to the denominator of the fraction.

↠⠀⠀x/(y + 8) = ¼

↠⠀⠀4x = y + 8

↠⠀⠀4x – y = 8⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀ ⠀ —eqₙ ( ii )

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

• E L I M I N A T I O N⠀M E T H O D :

↠⠀⠀ 3x – y = 3

↠⠀⠀ 4x – y = 8

↠⠀⠀ x = 5

Putting the value of x in eqₙ ( i ) :

↠⠀⠀ 3x – y = 3

↠⠀⠀ 3(5) – y = 3

↠⠀⠀ 15 – y = 3

↠⠀⠀ – y = 3 – 15

↠⠀⠀ – y = – 12

↠⠀⠀ y = 12

\begin{gathered}\rule{230px}{.2ex}\\\end{gathered}

❝ Therefore, the required fraction obtained is 5⁄12 ❞