Find the torque of a force F = -3 hat i + hat j + 5 hat k acting at the point r = 7 hat i + 3 hat j + hat k

Question

Find the torque of a force F = -3 hat i + hat j + 5 hat k acting at the point r = 7 hat i + 3 hat j + hat k (A) 14 hat i - 38 hat j + 16 hat k (B) 4 hat i + 4 hat j + 6 hat k (C) -14 hat i + 38 hat j - 16 hat k (D) -21 hat i + 3 hat j + 5 hat k

Tardigrade Admin · Accepted Answer

Torque is defined as the cross product of force vector

F

and

r

,
distance from the axis of rotation to the point on which the force is acting.

∴ τ = r \times F

Given

τ = 7 \hat{i} + 3 \hat{j} + \hat{k}

,

F = - 3 \hat{i} + \hat{j} + 5 \hat{k}

τ = ∣ ∣ \hat{i} 7 - 3 \hat{j} 31 \hat{k} 15 ∣ ∣

= \hat{i} (15 - 1) - \hat{j} (35 + 3) + \hat{k} (7 + 9)

= 14 \hat{i} - 38 \hat{j} + 16 \hat{k}

Q. Find the torque of a force $F = - 3 \hat{i} + \hat{j} + 5 \hat{k}$ acting at the point $r = 7 \hat{i} + 3 \hat{j} + \hat{k}$

$14 \hat{i} - 38 \hat{j} + 16 \hat{k}$

$4 \hat{i} + 4 \hat{j} + 6 \hat{k}$

$- 14 \hat{i} + 38 \hat{j} - 16 \hat{k}$

$- 21 \hat{i} + 3 \hat{j} + 5 \hat{k}$

Q. Find the torque of a force F=−3i^+j^​+5k^ acting at the point r=7i^+3j^​+k^

14i^−38j^​+16k^

4i^+4j^​+6k^

−14i^+38j^​−16k^

−21i^+3j^​+5k^

Torque is defined as the cross product of force vector F and r, distance from the axis of rotation to the point on which the force is acting. ∴τ=r×F Given τ=7i^+3j^​+k^, F=−3i^+j^​+5k^ τ=∣∣​i^7−3​j^​31​k^15​∣∣​ =i^(15−1)−j^​(35+3)+k^(7+9) =14i^−38j^​+16k^

Q. Find the torque of a force $F = - 3 \hat{i} + \hat{j} + 5 \hat{k}$ acting at the point $r = 7 \hat{i} + 3 \hat{j} + \hat{k}$

$14 \hat{i} - 38 \hat{j} + 16 \hat{k}$

$4 \hat{i} + 4 \hat{j} + 6 \hat{k}$

$- 14 \hat{i} + 38 \hat{j} - 16 \hat{k}$

$- 21 \hat{i} + 3 \hat{j} + 5 \hat{k}$