Gravitation Worksheet-7
(a) What will be the density of this solid?
(b) What will be the mass of water displaced by this solid?
(c) What will be the relative density of the solid?
(d) Will it float or sink in water?
Answer:
W = m × g
Here, weight of man on earth, W = 600 N
Mass of man on earth, m = ?
And, Acceleration due to gravity, g = 10 m s^{–2}
Now, putting these values in the above formula, we get :
600 = m × 10
m = 60 kg
Hence the mass of man on the earth is 60 kilograms. Since the mass of a body remains the same everywhere in the universe. So, the mass of this man on the moon will also be 60 kilograms.
Let’s calculate the value of acceleration due to gravity on the moon by using the same formula :
W = m × g
Now, weight of man on the moon, W = 100 N
Mass of the man on moon, m = 60 kg (Calculated)
And, Acceleration due to gravity, g = ?
(on the moon)
By putting these values in the formula, we get :
100 = 60 × g
So, g = 1.66 m s^{–2}
thus, the acceleration due gravity on the surface of the moon is 1.66 m s^{–2}.
Here, Mass of the man on moon, m = 70 kg
Acceleration due to gravity, g = 1.63 m/s^{2}
(on the moon)
We know that : W = m × g
So, W = 70 × 1.63
W = 114.1 N
Hence weight of the man will be 114.1 newtons on the moon. Since mass of a body is constant everywhere in the universe. The mass will be 70 kg on the earth as well as on the moon.
Here, Mass of the object = 50 g
And, Volume of the object = 20 cm^{3}
Density of object = 2.5 g/cm^{3}
Thus, the density of object is 2.5 g/cm^{3}. Since the density of the object is greater than the density of water so the object will sink in the water.
Relative density of substance
Here, Relative density of silver = 10.8
Density of silver = ?
Density of water = 1.0 × 10^{3} kg m^{–3}
So, Density of silver = 10.8 × 1.0 × 10^{3} kg m^{–3}
= 10.8 × 10^{3} kg m^{–3}
Thus, the density of silver in SI units is 10.8 × 10^{3} kg m^{–3}
= 1.42 g/cm^{3}.
(b) The solid will displace water equal to its own volume. Now, volume of water displaced is 350 cm^{3} and the density of water in is1 g/cm^{3}.
Density of water
We get, 1 g/cm^{3}
So, Mass of water = 1 g/cm^{3} × 350 cm^{3} = 350 g
Thus, the mass of water displaced is 350 grams.
(c) Relative density of solid
= 1.42
Thus, the relative density of the solid is 1.42.
(d) Since the relative density of this solid is greater than the relative density of water therefore, this solid is heavier than water so it will sink in water.