Final answer:
The mass of the necklace is approximately 0.0646 kg.
Step-by-step explanation:
In this problem, a meterstick balances at its center and when a necklace is suspended from one end, the balance point shifts. We can use the principle of moments to solve this problem. The principle of moments states that for an object in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Given that the balance point moves 9.5 cm toward the end of the meterstick, we can set up the equation:
M1 × d1 = M2 × d2
Where M1 and M2 are the masses of the meterstick and the necklace respectively, and d1 and d2 are the distances from the center of the meterstick to the balance point and the end with the necklace respectively.
Since the meterstick balances at its center, M1 = 0.34 kg.
Substituting the given values, we have:
(0.34 kg) × (0.095 m) = M2 × (0.5 m)
Solving for M2, the mass of the necklace, we find:
M2 = 0.34 kg × 0.095 m / 0.5 m = 0.0646 kg
Therefore, the mass of the necklace is approximately 0.0646 kg.