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 $12 \mathrm{~cm} \mathrm{mark}$, the stick is found to be balanced at $45 \mathrm{~cm}$. The mass of the metre stick is (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 $12 \mathrm{~cm} \mathrm{mark}$, the stick is found to be balanced at $45 \mathrm{~cm}$. The mass of the metre stick is
(a) $56 \mathrm{~g}$
(b) $66 \mathrm{~g}$
(c) $76 \mathrm{~g}$
(d) $86 \mathrm{~g}$

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Key Concepts

Lever Arm

The lever arm, or moment arm, is the perpendicular distance from the axis of rotation to the line of action of the force. It is a critical factor in calculating torque because the same force applied at different distances can result in different torques.

Center of Mass

The center of mass is the point in an object at which the mass can be considered to be concentrated. In uniform objects, it is typically at the geometric center, but additional masses can shift the overall center of mass, influencing the balance by altering the distribution of torque across the pivot point.

Torque

Torque, or moment of force, is the measure of the tendency of a force to rotate an object about a pivot or axis. It is calculated by multiplying the force by the perpendicular distance from the pivot point. In balance problems, the sum of the clockwise torques must equal the sum of the anticlockwise torques for the object to be in equilibrium.

Rotational Equilibrium

Rotational equilibrium occurs when the net torque acting on an object is zero, meaning there is no angular acceleration. This condition is essential in balance problems, as it allows an object to remain stationary without rotating.

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