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Q.

Four forces are acting on a particle. one force of magnitude 3 N is directed upward, another is directed 37o East of North having magnitude 5 N, third is directed in south-west direction is of magnitude 42N and fourth force is 5nN. If the particle is in equilibrium. The value on n is _______.

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answer is 2.

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Detailed Solution

Here, F→1=3k^F→2=5cos⁡37∘+5sin⁡37∘i^=4i^+3j^ and F→3=−42cos⁡45∘i^−42sin⁡45∘j^ =−4i^−4j^For equilibrium of the particle    F→1+F→2+F→3+F→4=0 or     3k^+3j^+4i^−4i^−4j^+F→4=0∴    F→4=j^−3k^∴    F→4=1+9=10∴    n=2
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