Units and Measurements

5%

Step 1: Write the formula for density. ρ = m / l³ Step 2: Apply the rule for error propagation in products and powers. For a quantity Z = xᵃ / yᵇ, the maximum percentage error is: (ΔZ/Z) × 100 = a(Δx/x) × 100 + b(Δy/y) × 100 Step 3: Identify the powers of each variable. Here, m has power 1 and l has power 3. Step 4: Calculate the maximum percentage error. (Δρ/ρ) × 100 = 1 × (Δm/m) × 100 + 3 × (Δl/l) × 100 = 1 × 2% + 3 × 1% = 2% + 3% = 5% Why other options are wrong: - 3%: Only adds 2% + 1%, ignoring the power of 3 for length. - 2%: Considers only the error in mass. - 1%: Considers only the

3.26 ly

Step 1: Recall the values of parsec and light year in metres. 1 parsec (pc) = 3.084 × 10¹⁶ m 1 light year (ly) = 9.46 × 10¹⁵ m Step 2: Convert parsec to light years. 1 pc = 3.084 × 10¹⁶ m / (9.46 × 10¹⁵ m/ly) = (3.084 / 9.46) × 10¹ ly = 0.326 × 10¹ ly = 3.26 ly Step 3: Interpretation. 1 parsec is the distance at which the Earth's orbital radius (1 AU) subtends an angle of 1 arc-second. It equals 3.26 light years. Why other options are wrong: - 1.50 ly: This is approximately 1 AU expressed differently — a confusion with AU. - 9.46 ly: This confuses the value of 1 light year (9.46 × 10¹⁵ m) w

4

Step 1: Apply the rules for significant figures one by one. Step 2: Leading zeros (zeros before the first non-zero digit) are NOT significant. In 0.006700, the zeros before 6 (i.e., 0.00) are leading zeros → NOT significant. Step 3: The digits 6, 7 are non-zero digits → SIGNIFICANT. Step 4: Trailing zeros AFTER the decimal point ARE significant. The two zeros after 7 (i.e., 00) are trailing zeros after the decimal → SIGNIFICANT. Step 5: Count the significant figures: 6, 7, 0, 0 → 4 significant figures. Why other options are wrong: - 7: This counts all digits including leading zeros, which

1%

Step 1: Write the formula for time period. T = 2π√(l/g) = 2π (l/g)^(1/2) = 2π × l^(1/2) × g^(-1/2) Step 2: Apply the error propagation rule for powers. (ΔT/T) × 100 = (1/2)(Δl/l) × 100 + (1/2)(Δg/g) × 100 Step 3: Since g is taken as exact, Δg = 0. (ΔT/T) × 100 = (1/2) × 2% + 0 = 1% The key concept here is that l appears as l^(1/2) (square root), so its power is 1/2, and the percentage error gets multiplied by 1/2. Why other options are wrong: - 2%: This forgets to multiply by the power 1/2; it directly takes the error in l. - 4%: This incorrectly multiplies by 2 instead of 1/2. - 0.5%: Thi