Question

A force (F) = `- 5hat"i" - 7hat"j" + 3hat"k"` acting on a particle causes a displacement (s) = `3hat"i" - 2hat"j" + "a"hat"k"` n its own direction. If the work done is 14 J, then the value of 'a' is ______.

विकल्प

• 0

• 5

• 15

• 1

Answer 1

A force (F) = `- 5hat"i" - 7hat"j" + 3hat"k"` acting on a particle causes a displacement (s) = `3hat"i" - 2hat"j" + "a"hat"k"` n its own direction. If the work done is 14 J, then the value of 'a' is 5.

Explanation:

Given, F = `- 5hat"i" - 7hat"j" + 3hat"k"`, 

s = `3hat"i" - 2hat"j" + "a"hat"k"`

and W = 14 J

The work done by a force in displacing a particle through a distance is given by

W = F · s     ....(i)

Substituting above values in Eq. (i), we get

`14 = (- 5hat"i" - 7hat"j" + 3hat"k") * (3hat"i" - 2hat"j" + "a"hat"k")`

`=> 14 = - 15 + 14 + 3"a"`

`=> "a" = 15/3` = 5