CBSE Class 7 Science Advanced Physics Measurements Long Answer Questions Set 02

Long Answer Questions

Question 1. Two identical containers A and B are filled with two different liquids of equal masses. The level of the liquid in container A is found to be one-fourth of the level of the liquid in container B. What is the ratio of the density of two liquids? If the density of the liquid in the container A is 2 g cm⁻³, then find the density of the mixture of the two liquids.
Answer:
Let the two containers be identical, so they have the same area of cross section. Let the masses of the liquids be equal, m_A = m_B = m.
Volume = area × height, so V_A = (1/4) V_B, that is, V_B = 4V_A.
Density = mass ÷ volume, so d_A ÷ d_B = V_B ÷ V_A = 4 ÷ 1.
Ratio of densities of A and B = 4 : 1.
d_A = 2 g cm⁻³, so d_B = 2 ÷ 4 = 0.5 g cm⁻³.
Mixture: total mass = m + m = 2m and total volume = V_A + 4V_A = 5V_A.
Density of the mixture = 2m ÷ 5V_A = (2 ÷ 5) × (m ÷ V_A) = (2 ÷ 5) × d_A = (2 ÷ 5) × 2 = 0.8 g cm⁻³.
In simple words: The liquid that fills only a quarter of the height is four times as dense; the mixture has twice the mass in five parts of the volume.

Teacher's Note:
1. Because the containers are identical, the heights are in the same ratio as the volumes.
2. The mixture's volume is assumed to be the sum of the two volumes.

Question 2. Three places A, B and C form the vertices of a triangle. A triangle to reduced scale is drawn as shown below. If the actual distance between A and C is 200 km, determine the actual distance from A to B and B to C.

Answer:
The scale of the drawing: AC = 10 cm on the triangle stands for 200 km, so 10 cm = 200 km.
1 cm = 200 ÷ 10 = 20 km.
AB = 5 cm, so the actual distance AB = 5 × 20 = 100 km.
BC = 8 cm, so the actual distance BC = 8 × 20 = 160 km.
In simple words: Find the number of km for 1 cm, then multiply each side of the drawing by it.

Teacher's Note:
1. Use the one side whose real length is known to get the scale.
2. The same scale applies to all three sides.

Question 3. Two persons A and B are 40 m apart. Triangulation method was used to measure the distance between a place C and the person A. The triangle obtained is as shown. The triangle is drawn from the positions of A and B and the vertices P, Q and R correspond to the positions of A, B and the place C, respectively. Determine the distance between the person A and the place C.

Answer:
Distance between A and B = 40 m, and on the triangle AB (= PQ) = 5 cm.
So 5 cm stands for 40 m, and 1 cm stands for 40 ÷ 5 = 8 m.
The distance between the person A and the place C is represented by PR = 6 cm.
Actual distance = 6 × 8 = 48 m.
In simple words: Find the real length of 1 cm of the drawing, then multiply it by the 6 cm side PR.

Teacher's Note:
1. P and Q are the positions of A and B.
2. Scale = real length ÷ drawn length.

Question 4. A physics student Ram was given an empty density bottle, a physical balance and a certain liquid. He first found the weight of empty density bottle to be 50 gf. When completely filled with water, it weighs 100 gf and when completely filled with a liquid, it weighs 130 gf. He calculated the density of the liquid. What could be his answer?
Answer:
Mass of the empty bottle = 50 g, so mass of water = 100 − 50 = 50 g and the volume of the bottle = 50 cm³.
Mass of the liquid = 130 − 50 = 80 g in the same volume of 50 cm³.
Density of the liquid = 80 ÷ 50 = 1.6 g cm⁻³ (1600 kg m⁻³).
In simple words: The water fixes the volume of the bottle; the liquid's mass divided by that volume is its density.

Teacher's Note:
1. gf and g are numerically equal here, since 1 gf is the weight of 1 g.
2. Always subtract the empty bottle's mass.

Question 5. Ram and Shyam were given cube A and cube B both having the same mass, respectively. The side of cube A is three times that of the cube B. Ram and Shyam found the densities of A and B. What is the ratio of densities of A and B?
Answer:
Let the side of cube B = l. Then the side of cube A = 3l.
Volume of A = (3l)³ = 27l³ and volume of B = l³.
Density = mass ÷ volume, and the masses are equal, so d_A ÷ d_B = V_B ÷ V_A = l³ ÷ 27l³.
Ratio of densities d_A : d_B = 1 : 27.
In simple words: A cube three times as long has 27 times the volume, so for the same mass its density is 27 times smaller.

Teacher's Note:
1. Volume goes as the cube of the side.
2. For equal masses, density is inversely proportional to volume.