Question

A force `vec"F"=(hat"i"+2hat"j"+3hat"k")`N acts at a point `(4hat"i"+3hat"j"-hat"k")`m. Then the magnitude of torque about the point `(hat"i" + 2hat"j" + hat"k")` m will be `sqrtx` N-m. The value of x is ______.

विकल्प

• 195

• 165

• 175

• 155

Answer 1

A force `vec"F"=(hat"i"+2hat"j"+3hat"k")`N acts at a point `(4hat"i"+3hat"j"-hat"k")`m. Then the magnitude of torque about the point `(hat"i" + 2hat"j" + hat"k")` m will be `sqrtx` N-m. The value of x is 195.

Explanation:

Given : `vec"F"=(hat"i"+2hat"j"+3hat"k")`N

And, `vec"r" = [(4hat"i"+3hat"j"-hat"k") -(hat"i" + 2hat"j" + hat"k")] = 3hat"i"+hat"j"-2hat"k"`

Torque, τ = `vec"r"xxvec"F"`

τ = `3hat"i"+hat"j"-2hat"k"xx(hat"i" + 2hat"j" + 3hat"k")`

τ = `|(hat"i",hat"j", hat"k"),(3,1,-2),(1,2,3)|`

= `7hat"i" -11hat"j"+5hat"k"`

Magnitude of torque, `|vecτ| = sqrt195`.