Equilibrium — Prelims Questions

A uniform ladder of length $L$ and mass $M$ leans against a smooth vertical wall, making an angle $\theta$ with the horizontal floor. The floor is rough. If the ladder is in static equilibrium, what is the minimum coefficient of static friction ($\mu_s$) required between the ladder and the floor?

A uniform plank of mass $m$ and length $L$ is supported at its ends by two scales. A person of mass $M$ stands at a distance $x$ from the left end. What are the readings on the left scale ($R_L$) and the right scale ($R_R$)?

A block of mass $m$ is suspended by two light strings, one making an angle of $30^\circ$ with the vertical and the other making an angle of $60^\circ$ with the vertical. What is the tension in the string making $30^\circ$ with the vertical?

Which of the following statements is TRUE regarding an object in dynamic equilibrium?

A uniform rod of length $L$ and mass $M$ is hinged at one end and held horizontally by a string attached to the other end, making an angle of $90^\circ$ with the rod. What is the tension in the string?

A block is sliding down a rough inclined plane at a constant velocity. Which of the following statements is true about the block?

An object is in stable equilibrium. If it is slightly displaced from its equilibrium position, what happens to its potential energy?