Subject : Physics - Example Questions - Torque and Equilibrium:

Question 1: Lever Balance

A uniform meter stick of mass M is placed on a fulcrum at the 60 cm mark. A 2 kg mass is hung at the 20 cm mark on one side, and a 3 kg mass is hung at the 90 cm mark on the other side. Determine the mass M of the meter stick. Assume the meter stick is of negligible mass.



Question 2: Hanging Rod Equilibrium

Consider a uniform rod of length L and mass M hanging horizontally from a ceiling. Two masses, m1 and m2, are attached at the ends of the rod. If m1 > m2, determine the point along the rod where it should be supported by a string attached to the ceiling for the system to be in equilibrium.



Kinetic Energy of Rotation:

Question 3: Rolling Hoop vs. Solid Disk

A solid disk and a hoop, both of the same mass and radius, are released from rest at the top of an inclined plane. Neglecting friction, compare their linear speeds at the bottom of the incline. Justify your answer using the conservation of energy.



Question 4: Rotating Rod

A thin rod of length L and mass M is rotating about its end with an angular velocity ω. Determine the kinetic energy of rotation of the rod.



Velocity on an Inclined Plane using Moment of Inertia:

Question 5: Rolling Down an Incline

A solid sphere of radius R and mass M starts from rest and rolls without slipping down an inclined plane of height h and angle θ. Calculate the velocity of the center of mass of the sphere when it reaches the bottom of the incline. Use the moment of inertia for a solid sphere.