Question

A force of -F `hat "k"` acts on the origin of the coordinate system. The torque about the point (2, - 1) is ____________.

विकल्प

• `-"F" (2 hat"i" + hat"j")`

• `"F" (hat"i" + 2 hat"j")`

• `-"F" (hat"i" - 2 hat"j")`

• `"F" (2 hat"i" - hat"j")`

Answer 1

A force of -F `hat k` acts on the origin of the coordinate system. The torque about the point (2, - 1) is `"F" (hat"i" + 2 hat"j")`.

Explanation:

`vec"F" = "F" hat"k"`

`vec"r" = (2hat"i" -hat"j")`

`hat tau = vec "r" xx vec "F"`

` = (2hat"i" -hat"j") xx (-"F"hat"k")`

`= -2"F" (hat"i" xx hat"k") + "F"(hat"j" xx hat"k")`

`= -2"F" (-hat"j") + "F"(hat"i") `

`Rightarrow 2"F"hat "j" + "F"hat "i"`

` = "F"(hat"i"+ 2hat"j")`