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Two forces 8N and 5N are acting at a poi...

Two forces 8N and 5N are acting at a point on a body at an angle `120^(@)` then find the (i) magnitude and (ii) direction of their resultant.

Text Solution

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Given : `P=8N,theta=5N,theta=120^(@)`
`theta=120^(@)`
`R=sqrt(P^2+Q^2+2PQcostheta)`
`sqrt(8^2+5^2+2xx8xx5cos120^(@))`
`R=sqrt(89-40)=7N`
direction `prop=tan^(-1)[(Qsintheta)/(P+Qcostheta)]` w.r.t `vecP" "prop=tan^(-1)[(5sin120^(@))/(8+5cos120^(@))]`
`prop=tan^(-1)[(5xx0.866)/(8-2.5)]" "prop=tan^(-1)(0.7872)`
Hence direction of R`=prop=38^(@)` w.r.t `vecP`
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Knowledge Check

  • Two equal forces (P each) act at a point inclined to cach other at an angle of 120^(@) . The magnitude of their resultant is

    A
    `P//2`
    B
    `P//4`
    C
    `P`
    D
    `2P`

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