1.A measuring cylinder contains 30 cm³ of liquid. When a stone of weight 0.92 N is dropped into the liquid, it sinks to the bottom and the liquid level rises to the 70 cm³ graduation. Taking the weight of 1 kg to be 10 N, calculate

(i) The mass of the stone,

(ii) The density of the stone.

Explain why it would not be possible to use this method to determine the density of cork which would float in the liquid.

Ans.

(i) Mass, m=W/g

=0.92/10

=0.092kg

(ii) volume of stone = change of reading on measuring cylinder

=70-30

=40cm³

Density of stone = mass of stone/volume of stone

= 92/40

= 2.3g/cm³

To find the volume of the cork accurately, it needs to be immersed completely into the liquid. Since the cork floats in the liquid, the volume of the liquid displaces would not be equal to the volume of the cork. Thus it would not be possible to use this method to determine the density of cork.

2.The mass of 600 spherical lead pellets is found to be 66g and the total volume of the pellets is found to be 5.7cm³. Calculate

(i) the total weight of the pellets

(ii) the volume of one pellets,

(iii) the density of the pellets in kg/m³,

(iv) the number of pellets which has a mass of 1.00 kg. The force of gravity acting on a mass of 1.00 kg is 10.0 N

Ans.

(i) weight of the pellets = mg

= (66/1000) x 10

= 0.66 N

(ii) volume of one pellets = 5.7/600

= 9.5 x 10^-3 cm³

= 9.5 x 10^-9 m³

(iii) density of the pellets = total mass/ total volume

= 66/5.7

= 11.6 g/ cm³

= 11.6 x 10³ kg/ m³

(iv) number of pellets = 1.00 / (0.066 / 600)

= 9090 (3 s.f.)

3.The acceleration due to gravity near the surface of the moon is 1.6 m s ^–2.

(a) what is the gravitational field strength?

(b) What is the weight of an astronaut on the moon if his mass is 80 kg?

Ans.

(a) gravitational field strength = acceleration due to gravity

= 1.6 N kg^-1

(b) weight = mg

= 80 kg x 1.6 m s^-2

= 128 N

4. The table below shows the densities of a few substances.

(a) A cork will float in water, honey and oil.

(b) Water will float in honey.

(c) When we have honey, oil and water in a glass, oil will be at the top layer, followed by honey and water will be at the bottom of the glass.

(d) Carbon is denser than gold.

(e) Glass will float on honey.

(f) When we have mayonnaise, oil and water in a glass, mayonnaise will be on top, followed by oil and then water.

Ans.

(a) True

(b) True

(c) False

(d) False

(e) False

(f) True

5. Two balls of different materials are of the same size. Do they necessarily have the same weight? Explain.

Ans.

Two balls of the same size need not have the same weight. The reason behind is because they are made of different materials and hence, they have different densities.

From the equation density = mass/volume, we get mass = density x volume.

Therefore, even though the two balls have the same volume, different densities will cause them to have different masses. Since weight = mass x gravitational field strength, hence, the two balls will have different weights.

6. Objects A and B are thrown into the sea. Object A floats but object B sinks. When the two objects are thrown into a swimming pool, both of them sink. Given that the densities of sea water and water in the swimming pool are 1000 kg/m³ and 1030 kg/m³ respectively, what can be concluded about the densities of object A kg/m³ and object B kg/m³?

Ans.

Since object A floats in sea water buy sinks in pure water, we know that it is less dense than sea water but denser than pure water. Since object B sinks in both sea and pure water, object B is denser than sea water. Hence, we conclude that the density of object A is between the densities of pure water and sear water. The density of object B is higher than of sea water and pure water.