The length of the uniform meter stick is 50 cm and the mass of the uniform meter stick is 50 g.
A sketch of the uniform stick and the mass
The sketch of the uniform stick and the mass will be two based on the given statement.
when the uniform stick balances on knife at 10 cm from one end;
-------------------------------------------------------
↓ 10cm Δ (L - 10 cm) ↓
200g M
When the knife edge is moved 5 cm further
|---------------15 cm-----------------|
-----------------------------------------------------------------------
↓ 8.75 cm Δ (L - 15 cm) ↓
200g M
From the first diagram, apply principle of moment;
200(10) = M(L - 10) ------- (1)
From the second diagram, apply principle of moment;
200(8.75) = M(L - 15) ------- (2)
From equation (1); M = (2000) / (L - 10)
From equation (2); M = (1750) / (L - 15)
Solve (1) and (2);
(2000) / (L - 10) = (1750) / (L - 15)
1750(L - 10) = 2000(L - 15)
L - 10 = 2000/1750(L - 15)
L - 10 = 1.143(L - 15)
L - 10 = 1.143L - 17.14
17.14 - 10 = 1.143L - L
7.14 = 0.143L
L = 7.14/0.143
L = 50 cm
Mass of the uniform stick
M = (2000) / (50 - 10)
M = 50 g
Thus, the length of the uniform meter stick is 50 cm and the mass of the uniform meter stick is 50 g.
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