The torque of a force 5 î+3 ĵ-7 k̂ about the origin is τ. If the force acts on a particle whose position vector is 2 i+2 j+k, then the value of τ will be

Solution

Physics sir · 3 steps

Torque is r⃗ × F⃗, in that order. Set up the determinant and expand it row by row.

1. Set up. Torque about the origin is τ⃗ = r⃗ × F⃗, with r⃗ = 2î + 2ĵ + k̂ and F⃗ = 5î + 3ĵ - 7k̂. Put r⃗ in the second row and F⃗ in the third, because order matters in a cross product.

   τ⃗ = |î, ĵ, k̂; 2, 2, 1; 5, 3, -7|

2. Expand. î: (2)(-7) - (1)(3) = -14 - 3 = -17. ĵ: -[(2)(-7) - (1)(5)] = -(-14 - 5) = 19. k̂: (2)(3) - (2)(5) = 6 - 10 = -4.
3. So. τ⃗ = -17î + 19ĵ - 4k̂, which is option (c).

The idea to keep. For torque, always write r⃗ × F⃗, never the reverse. In the determinant, remember the minus sign in front of the ĵ term, and check each component separately.

Answer from the NTA final answer key. Solution by PrepWiser.