Question

A force F=6 i ˉ +2 j ˉ ​+3 k acts on a particle and produces a displacement of s =2 i −3 j −x k . If the work done is zero, the value of x is:

Answer 1

If the work done is zero, value of x= 2

Explanation:

• Work is said to be done by any body if it changes its position under the influence of force. It is given as dot or scalar product of force and displacement covered by the body. Work is a scalar quantity as it is dot product of two vector quantities force and displacement. Work gives only magnitude and have SI unit J (joule)

                          Work done = Force . Distance

                              W = F.s

                               W = F s cosΘ

where Θ = angel between force applied and distance covered

Given, Work done = 0

Force F = 6 i +2 j +3 k

distance s = 2 i - 3 j - x k

=> work = F.s

=> 0 = ( 6 i +2 j +3 k) .(2 i - 3 j - x k)

=> 0 = 12 - 6 - 3 x

=> 3 x= 12- 6

=> 3 x = 6

=> x = 2

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Answer 2

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if the workdone is zero then x=2