A force of $$1000$$ N in a particular direction must be applied to a block. For same reason. It is not possible to apply the force in that direction but two forces can be applied to $$30o$$ and $$45o$$ on either side of it in the same plane containing the given force. If the ratio of magnitude of forces as n The value of n $$is_______$$.

Question

A force of $$1000$$ N in a particular direction must be applied to a block. For same reason. It is not possible to apply the force in that direction but two forces can be applied to $$30o$$ and $$45o$$ on either side of it in the same plane containing the given force. If the ratio of magnitude of forces as n The value of n $$is_______$$.

Infinity Learn · Accepted Answer

The resultant of $$F1$$ and $$F2$$ is in direction of $$1000$$ N force. So, the sum of component of $$F1$$ and $$F2$$ in perpendicular direction of $$1000$$ N force will be zero.∴ $$F1sin$$⁡$$30$$∘$$=F2sin$$⁡$$45$$∘ or  $$F1F2=$$$$sin$$⁡$$45$$∘$$sin$$⁡$$30$$∘$$=12$$×$$12=2$$∴ $$n=2$$

Scalars and Vectors

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Scalars and Vectors

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The resultant of F1 and F2 is in direction of 1000 N force. So, the sum of component of F1 and F2 in perpendicular direction of 1000 N force will be zero.∴ F1sin⁡30∘=F2sin⁡45∘ or F1F2=sin⁡45∘sin⁡30∘=12×12=2∴ n=2

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