Question

A student wishes to determine the density ρ of lead. She measures the mass and diameter of a small sphere of lead:
mass = (0.506 ± 0.005) g diameter = (2.20 ± 0.02) mm.
What is the best estimate of the percentage uncertainty in her calculated value of ρ ? A 1.7% B 1.9% C 2.8% D 3.7%

Answer 1

Answer:

Sky-diver jumps from high-altitude balloon.

(a) Explain briefly why acceleration of the sky-diver

(i) decreases with time

(ii) is 9.8 ms-2 at start of the jump

(b) Variation with time t of the vertical speed v of sky-diver is shown.

Use Fig to determine magnitude of the acceleration of sky-diver at time t = 6.0 s.

(c) Sky-diver and his equipment have a total mass of 90 kg.

(i) Calculate, for sky-diver and his equipment,

1. total weight

2. accelerating force at time = 6.0s

(ii) Use answers in (i) to determine total resistive force acting on sky-diver at time

Explanation:

please mark me as brainlest if the answer is correct

Answer 2

The answer is 3.7%

GIVEN

A student wishes to determine the density ρ of lead. She measures the mass and diameter of a small sphere of lead:

mass = (0.506 ± 0.005) g diameter = (2.20 ± 0.02) mm.

TO FIND

The estimate of the percentage uncertainity in density.

SOLUTION

We can simply solve the above problem as follows;

We know that the formula to calculate density if as follows;

Density = Mass/volume

Mass of the lead sphere = 0.506 ± 0.005

Diameter of the sphere = 2.20 ± 0.02 mm.

Volume of the sphere = (4/3)πr³

We know,

Radius = diameter/2

Therefore,

Volume = πd³/6

$Density(ρ) = \frac{m}{ \frac{\pi \: d^{3} }{6} } = \frac{6m}{\pi \: d ^{3} }$

Now,

$\frac{Δ}{?} = ( \frac{Δm}{m} + 3 \times \frac{Δd}{d} )$

Percentage uncertainity in density;

$\frac{Δρ}{ρ} \times 100 = ( \frac{Δm}{m} + 3 \times \frac{Δd}{d} ) \times 100$

Putting the values of Δm, m, Δd and Δd in the above formula we get,

$= ( \frac{0.005}{0.506} + 3 \times \frac{0.02}{2.20} ) \times 100$

(0.009 + 0.027)× 100

Δρ = 3.7%

Hence, The answer is 3.7%

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