A force of -Pk acts on the origin of the coordinate system. The torque about the point (2, -3) is P(ai + bj). The ratio of a/b is x/2. The value of x is ___________. Numerical answer type. Work it out, then open the answer.

Answer: 3. Force acts at origin, so r = O - (2,-3,0) = -2i+3j. τ = (-2i+3j)×(-Pk) = 2P(i) - 3P(j) = -2Pj - 3Pi a = -3, b = -2, so a/b = 3/2 = x/2 x = 3

A force of -Pk acts on the origin of the coordinate system. The… | JEE Main 2023 (10 Apr, Shift 2)

Q16JEE Main 2023 · 10 APR · SHIFT 2Medium

Torque, Couple & Equilibrium of Rigid Bodies

A force of $-P\hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2, -3)$ is $P(a\hat{i} + b\hat{j})$ . The ratio of $\frac{a}{b}$ is $\frac{x}{2}$ . The value of $x$ is ___________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 3

Force acts at origin, so $\vec{r} = O - (2,-3,0) = -2\hat{i}+3\hat{j}$ .
$\vec{\tau} = (-2\hat{i}+3\hat{j})\times(-P\hat{k}) = 2P(\hat{i}\times\hat{k}) - 3P(\hat{j}\times\hat{k}) = -2P\hat{j} - 3P\hat{i}$
$a = -3$ , $b = -2$ , so $\frac{a}{b} = \frac{3}{2} = \frac{x}{2}$
x = 3

Report a mistake

Torque, Couple & Equilibrium of Rigid Bodies question from JEE Main 2023 (10 Apr, Shift 2)

More questions on Torque, Couple & Equilibrium of Rigid Bodies