A student is asked to find the volume of a small irregularly shaped piece of rock. The student has a balance, a measuring cylinder containing water, and a ruler available.
Which apparatus must the student use to find the volume of the small piece of rock?
Correct Answer: \( \boxed{\mathrm{D}} \)
The volume of an irregularly shaped object is measured using the water displacement method.
A ruler cannot be used because the rock does not have regular dimensions from which a volume formula can be applied.
A balance measures mass, not volume, so it is not required for this measurement.
First, record the initial water level \(V_1\) in the measuring cylinder.
Then immerse the rock completely and record the new water level \(V_2\).
The volume of the rock is:
\( V_{\mathrm{rock}} = V_2 – V_1 \)
Therefore, only the measuring cylinder is needed to determine the volume of the irregularly shaped rock.
Hence, the correct answer is (D).
Four hollow glass balls, P, Q, R and S, each have a volume of \(30\,\mathrm{cm^3}\).
The mass of each ball is shown in the table.
Which balls will float in a liquid of density \(0.95\,\mathrm{g/cm^3}\)?
Correct Answer: \( \boxed{\mathrm{A}} \)
An object floats if its density is less than the density of the liquid.
Density is calculated using:
\( \rho=\frac{m}{V} \)
For ball P: \( \rho_P=\frac{15}{30}=0.50\,\mathrm{g/cm^3} \)
For ball Q: \( \rho_Q=\frac{25}{30}\approx0.83\,\mathrm{g/cm^3} \)
For ball R: \( \rho_R=\frac{35}{30}\approx1.17\,\mathrm{g/cm^3} \)
For ball S: \( \rho_S=\frac{45}{30}=1.50\,\mathrm{g/cm^3} \)
The liquid density is \(0.95\,\mathrm{g/cm^3}\).
Since \(0.50 < 0.95\) and \(0.83 < 0.95\), balls P and Q float.
Balls R and S have densities greater than the liquid density, so they sink.
Therefore, the balls that will float are P and Q.
Hence, the correct answer is (A).
Which piece of equipment is useful in determining the density of an irregularly-shaped stone?
Correct Answer: \( \boxed{\mathrm{C}} \)
Density is defined as:
\( \rho = \frac{m}{V} \)
To determine the density of an irregularly-shaped stone, both its mass and volume must be known.
The volume of an irregular object cannot be measured accurately using a metre ruler. Instead, the displacement method is used.
The stone is submerged in water, and the increase in water level gives the volume of the stone.
A measuring cylinder is required to measure this change in volume accurately.
A stop-watch measures time, and a voltmeter measures potential difference, so neither is useful for finding density.
Therefore, the correct equipment is the measuring cylinder.
Hence, the correct answer is (C).
