Question

The line of action of Force F=(i-2j)N passes through the point whose vector is (-J+k)m. The moment of F about the origin in Nm is:

a)0Nm
b)(2j+j)Nm
c)(i+i+k)Nm
d)(i+2)+kNm

Answer 1

The moment of the force F about the origin, calculated using the cross-product of the position vector r and force vector F, is (i+2j+k)Nm, corresponding to option d.

Step-by-step explanation:

The question refers to the concept of moment of a force, also known as torque in physics. To find the moment of force F about the origin, we use the cross-product of the position vector (r) with the force vector (F). In this case, the position vector is r = -j + k and the force vector is F = i - 2j. The moment (torque) M is given by the cross product r × F.

M = r × F = | i j k |
0 -1 1
1 -2 0 |

Calculating the determinant, we find:
M = -(i (0) - k (2)) - j (0 - k (1)) + k (i (-1) - j (1))
M = i +(2j) + kNm

So the correct answer is option d) (i+2)+kNm.