Torque — MCQ Practice

A force \\vec{F} = (3\hat{i} + 2\hat{j} - 4\hat{k})\,\text{N}\ is applied at a point whose position vector is \\vec{r} = (\hat{i} - 2\hat{j} + \hat{k})\,\text{m}\ with respect to the origin. Calculate the torque \\vec{\tau}\ about the origin.

A uniform rod of length $L$ and mass $M$ is pivoted at one end. A force $F$ is applied at the free end, perpendicular to the rod. What is the initial angular acceleration of the rod?

A wheel of radius $R=0.2,\text{m}$ and moment of inertia I=0.5,\text{kg\\cdot\m}^2 is free to rotate about its axis. A tangential force of $10,\text{N}$ is applied to its rim. What is the angular acceleration of the wheel?

A uniform meter stick of mass $150,\text{g}$ is pivoted at the $40,\text{cm}$ mark. A $200,\text{g}$ mass is suspended at the $10,\text{cm}$ mark. Where should a $500,\text{g}$ mass be suspended to balance the meter stick?

Which of the following statements about torque is INCORRECT?

A particle of mass $m$ is projected with velocity $v$ from the origin at an angle \\theta\ with the horizontal. What is the torque of the gravitational force about the origin when the particle is at its highest point?

A uniform circular disc of mass $M$ and radius $R$ is rotating about its central axis with angular velocity \\omega\. A constant braking torque \\tau_b\ is applied to the disc. How long will it take for the disc to come to rest?

A force \\vec{F} = (2\hat{i} + 3\hat{j})\,\text{N}\ acts on a particle. If the position vector of the particle is \\vec{r} = (\hat{i} - \hat{j})\,\text{m}\, what is the magnitude of the torque about the origin?