In a certain beam balance the centre of gravity of the beam lies a small vertical…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
In a certain beam balance the centre of gravity C of the beam lies a small vertical distance h below the knife-edge K.
(i) Explain why, when the beam is given a small angular displacement θ, it performs small oscillations about its equilibrium position.
(ii) Derive an expression for the restoring couple acting on the beam in terms of h, the mass of the beam mb, and the angular displacement θ.
(iii) Discuss qualitatively how the magnitude of h affects (a) the stability and (b) the sensitivity of the balance, and state the practical compromise adopted in design.