The force 7 hat i + 3 hat j- 5 hat k acts on a particle whose position vector is hat i - hat j + hat k . What is the torque of a given force about the origin?

Question

The force 7 hat i + 3 hat j- 5 hat k acts on a particle whose position vector is hat i - hat j + hat k . What is the torque of a given force about the origin? (A) 2 hati +12 hatj +10 hatk (B) 2 hati +10 hatj +12 hatk (C) 2 hati +10 hatj +10 hatk (D) 10 hati +2 hatj + hatk

Tardigrade Admin · Accepted Answer

Here, vecr = hati - hatj + hatk , vecF = 7 hati +3 hatj -5 hatk Torque, vecτ = vecr × vecF vecτ = | hati& hatj& hatk 1&-1&1 7&3&-5| = hati (5-3) + hatj (7-(-5)) + hatk (3-(-7)) or vecτ = 2 hati +12 hatj +10 hatk

Q. The force $7 \hat{i} + 3 \hat{j} - 5 \hat{k}$ acts on a particle whose position vector is $\hat{i} - \hat{j} + \hat{k}$ . What is the torque of a given force about the origin?

$2 \hat{i} + 12 \hat{j} + 10 \hat{k}$

$2 \hat{i} + 10 \hat{j} + 12 \hat{k}$

$2 \hat{i} + 10 \hat{j} + 10 \hat{k}$

$10 \hat{i} + 2 \hat{j} + \hat{k}$

Here, $r = \hat{i} - \hat{j} + \hat{k}, F = 7 \hat{i} + 3 \hat{j} - 5 \hat{k}$
Torque, $τ = r \times F$
$τ = ∣ ∣ \hat{i} 17 \hat{j} - 1 3 \hat{k} 1 - 5 ∣ ∣$
$= \hat{i} (5 - 3) + \hat{j} (7 - (- 5)) + \hat{k} (3 - (- 7))$
or $τ = 2 \hat{i} + 12 \hat{j} + 10 \hat{k}$

Q. The force 7i^+3j^​−5k^ acts on a particle whose position vector is i^−j^​+k^ . What is the torque of a given force about the origin?

2i^+12j^​+10k^

2i^+10j^​+12k^

2i^+10j^​+10k^

10i^+2j^​+k^