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A uniform wooden lath 100 cm long and mass 95 g is balanced on a knife edge when a 5 g mass is hung 10 cm from one end. How far is the knife edge from the center of gravity of the lath?

Answer :

Final answer:

The knife edge is located 5cm to the left of the center of gravity of the wooden lath

Explanation:

To find the distance of the knife edge from the center of gravity of the wooden lath, we can use the principle of moments. The torque exerted by the 5g mass hanging 10cm from one end can be balanced by the torque exerted by the lath. The torque is given by the product of the force and the perpendicular distance from the pivot point. Since the wooden lath is uniform, the center of gravity is at its midpoint. Let's denote the distance of the knife edge from the center of gravity as x. The torque exerted by the hanging mass can be calculated as follows:

Torque = 5g * 10cm = 5 * 10 * 10-3 kg * m

The torque exerted by the lath can be calculated as follows:

Torque = (95g * x) + (5g * (100cm - x)) = (95 * x * 10-3) + (5 * (100 - x) * 10-3) kg * m

Setting up the equation and solving for x:

(95 * x * 10-3) + (5 * (100 - x) * 10-3) = 5 * 10 * 10-3

95x + 500 - 5x = 50

90x = -450

x = -5

The negative value of x indicates that the knife edge is 5cm to the left of the center of gravity of the lath.

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Rewritten by : Barada