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  4. If the resultant of two unlike parallel forces of magnitudes 10 N and 16 N act along a line at a distance of 24 cm from the line of action of the smaller force is 8 N, then the distance between the lines of action of the force is:

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Q. If the resultant of two unlike parallel forces of magnitudes $10 \,N$ and $16 \,N$ act along a line at a distance of $24 \,cm$ from the line of action of the smaller force is $8\, N$, then the distance between the lines of action of the force is:

Bihar CECEBihar CECE 2005

Solution:

Let the forces of magnitudes $10\,N$ and $16 \,N$ be acting at A and B respectively. Suppose the resultant acts at C. Then
image
Taking moment of forces about B.
$ 10.x=8.(24-x) $
$ \Rightarrow $ $ 10x=192-8x $
$ \Rightarrow $ $ 18x=192 $
$ \Rightarrow $ $ x=10.66\,cm $