Question

A uniform meter rule of mass 90g is pivoted at the 40cm mark. If the rule is in equilibrium with an unknown mass m placed at the 10cm mark and a 72g mass at the 70cm mark. Determine m​

Answer 1

To find the mass of the unknown m, we can use the principle of torque balance. By setting up an equation using the torques created by the unknown mass m and the 72g mass, we can solve for m. The mass of the unknown m is equal to -72g.

Step-by-step explanation:

To find the value of m, we can use the principle of torque balance. In this case, the rule is in equilibrium, which means that the total torque acting on it is zero. The torque is the product of the force and the perpendicular distance from the pivot to the line of action of the force.

For the rule to be in equilibrium, the torques created by the unknown mass m and the 72g mass must balance out. Since the rule is pivoted at the 40cm mark, the perpendicular distance for the 90g mass is 30cm (40cm - 10cm) and for the 72g mass is -30cm (40cm - 70cm).

Using the principle of torque balance:

Torque due to m = Torque due to 72g mass

m * 30cm = 72g * (-30cm)

Solving for m, we get:

m = 72g * (-30cm) / 30cm = -72g