Question

1. Two forces F = 2î +39 – 4k and Fx = i + j - k acting on
a particle causes it to shift from (1, 2, 3) to (2, 4, 5). The work
done by resultant force is
(1) 1 J
(2) 2 J
(3) 3 J
(4) 4J​

Answer 1

Explanation:

we know that

work done, w=F.d

F'=2î+3j-4k

F"=i+j-k

therefore, F net =(2i+3j-4k)+(i+j-k)

=3i+4j-5k

Let ds =dx i + dy j + dz k

W=F.ds

=(3i+4j-5k).(dx i+ dy j+ dz k)

=3dx + 4dy - 5dz

integrating dx from 1 to 2

dy from 2 to 4

dz from 3 to 5

=3[2-1] + 4[4-2] -5[5-3]

=3 + 4*2 + 5*2

=3 + 8 - 10

=1J