A metre stick is balanced on a knife edge at its centre....

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass $5 \mathrm{~g}$ are put one on top of the other at the $12.0 \mathrm{~cm}$ mark, the stick is found to be balanced at $45.0 \mathrm{~cm}$. What is the mass of the metre stick? (a) $56 \mathrm{~g}$ (b) $66 \mathrm{~g}$ (c) $76 \mathrm{~g}$ (d) $86 \mathrm{~g}$

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass $5 \mathrm{~g}$ are put one on top of the other at the $12.0 \mathrm{~cm}$ mark, the stick is found to be balanced at $45.0 \mathrm{~cm}$. What is the mass of the metre stick?
(a) $56 \mathrm{~g}$
(b) $66 \mathrm{~g}$
(c) $76 \mathrm{~g}$
(d) $86 \mathrm{~g}$

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Key Concepts

Torque

Torque, or moment of force, is the product of the force applied and the distance from the pivot point at which the force is applied. It determines how much rotational effect a force produces about a specific axis, and it is fundamental in solving balance problems where forces cause rotation.

Lever Arm

The lever arm is the perpendicular distance between the line of action of a force and the pivot point. It plays a crucial role in calculating torque, as even a small force can result in a large torque if applied at a long lever arm.

Equilibrium

Equilibrium in a rotational context means that the net torque (the sum of all torques acting on the system) is zero, so there is no angular acceleration. This condition is essential in balance problems, where the moments (torques) caused by all forces must counterbalance each other.

Center of Mass

The center of mass is the point at which the mass of an object can be considered to be concentrated. When additional masses are added to a system, the overall center of mass shifts depending on the location and magnitude of these masses, which in turn affects the balance of the system.

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