Answer :
Let's break down the given physics questions and provide detailed, step-by-step solutions.
### Question 1:
Given:
- Heat energy, [tex]\( Q \)[/tex]
- Specific heat capacity, [tex]\( S \)[/tex]
- Change in temperature, [tex]\( dt \)[/tex]
Which of the following formulas is correct to calculate mass, [tex]\( m \)[/tex]?
(i) [tex]\( m = \frac{S \times dt}{Q} \)[/tex]
(ii) [tex]\( m = \frac{Q \times dt}{S} \)[/tex]
(iii) [tex]\( m = \frac{dt}{Q \times S} \)[/tex]
(iv) [tex]\( m = \frac{Q}{S \times dt} \)[/tex]
#### Solution:
The relationship between heat energy, specific heat capacity, mass, and change in temperature is given by:
[tex]\[ Q = m \times S \times dt \][/tex]
Rearranging to solve for mass [tex]\(m\)[/tex]:
[tex]\[ m = \frac{Q}{S \times dt} \][/tex]
Therefore, the correct formula to calculate the mass [tex]\( m \)[/tex] is:
(iv) [tex]\( m = \frac{Q}{S \times dt} \)[/tex]
### Question 2:
In which of the following conditions is the total number of electrons 10?
(i) [tex]\( O^{-} \)[/tex]
(ii) [tex]\( Mg \)[/tex]
(iii) [tex]\( Na^{+} \)[/tex]
(iv) [tex]\( N^{-} \)[/tex]
#### Solution:
- For [tex]\( O^{-} \)[/tex]: Oxygen has 8 protons (atomic number 8) and gains 1 electron to become [tex]\( O^{-} \)[/tex]. So, the number of electrons = 8 + 1 = 9.
- For [tex]\( Mg \)[/tex]: Magnesium has 12 protons (atomic number 12). If it is neutral, the number of electrons = 12.
- For [tex]\( Na^{+} \)[/tex]: Sodium has 11 protons (atomic number 11) and loses 1 electron to become [tex]\( Na^{+} \)[/tex]. So, the number of electrons = 11 - 1 = 10.
- For [tex]\( N^{-} \)[/tex]: Nitrogen has 7 protons (atomic number 7) and gains 1 electron to become [tex]\( N^{-} \)[/tex]. So, the number of electrons = 7 + 1 = 8.
Therefore, the correct condition where the total number of electrons is 10 is:
(iii) [tex]\( Na^{+} \)[/tex]
### Question 3:
Which of the following is the correct molecular formula for the given structural formula?
(i) [tex]\( C_3H_6(OH)_2 \)[/tex]
(ii) [tex]\( C_3H_5(OH)_3 \)[/tex]
(iii) [tex]\( C_3H_2(OH)_2 \)[/tex]
(iv) None of the above
#### Solution:
To verify the correct molecular formula, we must match the structural formula with the correct option:
- [tex]\( C_3H_6(OH)_2 \)[/tex]: This implies the molecule has 3 carbon atoms, 6 hydrogen atoms, and 2 hydroxyl groups (-OH).
- [tex]\( C_3H_5(OH)_3 \)[/tex]: This implies 3 carbon atoms, 5 hydrogen atoms, and 3 hydroxyl groups.
- [tex]\( C_3H_2(OH)_2 \)[/tex]: This implies 3 carbon atoms, 2 hydrogen atoms, and 2 hydroxyl groups.
Based on typical organic chemical structures, and without the actual structure being provided here, the most standard matching options would be:
(i) [tex]\( C_3H_6(OH)_2 \)[/tex]
### Question 4:
In the figure, the bee of condition B is converted to pupa in 5.5 days. Which type of honey bee can it form?
(i) Worker bee
(ii) Drone bee
(iii) Queen bee
(iv) Queen and worker bee
#### Solution:
- Worker bees are usually female and non-reproductive, with developmental periods generally ranging around 21 days.
- Drone bees are male and develop in about 24 days.
- Queen bees, which are reproductive females, develop in the shortest period, typically around 16 days.
Given that the bee in condition B is converted to a pupa in 5.5 days, this matches the developmental period typical for:
(iii) Queen bee
### Question 5:
When the mass of two bodies remains constant, and the distance between them is doubled, what will be the gravitational force exerted between them?
(i) [tex]\( F = G \frac{m_1 \cdot m_2}{d^2} \)[/tex]
(ii) [tex]\( F = G \frac{m_1 \cdot m_2}{2d^2} \)[/tex]
(iii) [tex]\( F = 2G \frac{m_1 \cdot m_2}{d^2} \)[/tex]
(iv) [tex]\( F = G \frac{m_1 \cdot m_2}{4d^2} \)[/tex]
#### Solution:
The gravitational force between two bodies is given by Newton's law of gravitation:
[tex]\[ F = G \frac{m_1 \cdot m_2}{d^2} \][/tex]
If the distance [tex]\( d \)[/tex] is doubled, the new distance becomes [tex]\( 2d \)[/tex]. The new force [tex]\( F_{\text{new}} \)[/tex] is:
[tex]\[ F_{\text{new}} = G \frac{m_1 \cdot m_2}{(2d)^2} = G \frac{m_1 \cdot m_2}{4d^2} \][/tex]
Therefore, the gravitational force becomes one-fourth of its original value:
(iv) [tex]\( F = G \frac{m_1 \cdot m_2}{4d^2} \)[/tex]
### Question 1:
Given:
- Heat energy, [tex]\( Q \)[/tex]
- Specific heat capacity, [tex]\( S \)[/tex]
- Change in temperature, [tex]\( dt \)[/tex]
Which of the following formulas is correct to calculate mass, [tex]\( m \)[/tex]?
(i) [tex]\( m = \frac{S \times dt}{Q} \)[/tex]
(ii) [tex]\( m = \frac{Q \times dt}{S} \)[/tex]
(iii) [tex]\( m = \frac{dt}{Q \times S} \)[/tex]
(iv) [tex]\( m = \frac{Q}{S \times dt} \)[/tex]
#### Solution:
The relationship between heat energy, specific heat capacity, mass, and change in temperature is given by:
[tex]\[ Q = m \times S \times dt \][/tex]
Rearranging to solve for mass [tex]\(m\)[/tex]:
[tex]\[ m = \frac{Q}{S \times dt} \][/tex]
Therefore, the correct formula to calculate the mass [tex]\( m \)[/tex] is:
(iv) [tex]\( m = \frac{Q}{S \times dt} \)[/tex]
### Question 2:
In which of the following conditions is the total number of electrons 10?
(i) [tex]\( O^{-} \)[/tex]
(ii) [tex]\( Mg \)[/tex]
(iii) [tex]\( Na^{+} \)[/tex]
(iv) [tex]\( N^{-} \)[/tex]
#### Solution:
- For [tex]\( O^{-} \)[/tex]: Oxygen has 8 protons (atomic number 8) and gains 1 electron to become [tex]\( O^{-} \)[/tex]. So, the number of electrons = 8 + 1 = 9.
- For [tex]\( Mg \)[/tex]: Magnesium has 12 protons (atomic number 12). If it is neutral, the number of electrons = 12.
- For [tex]\( Na^{+} \)[/tex]: Sodium has 11 protons (atomic number 11) and loses 1 electron to become [tex]\( Na^{+} \)[/tex]. So, the number of electrons = 11 - 1 = 10.
- For [tex]\( N^{-} \)[/tex]: Nitrogen has 7 protons (atomic number 7) and gains 1 electron to become [tex]\( N^{-} \)[/tex]. So, the number of electrons = 7 + 1 = 8.
Therefore, the correct condition where the total number of electrons is 10 is:
(iii) [tex]\( Na^{+} \)[/tex]
### Question 3:
Which of the following is the correct molecular formula for the given structural formula?
(i) [tex]\( C_3H_6(OH)_2 \)[/tex]
(ii) [tex]\( C_3H_5(OH)_3 \)[/tex]
(iii) [tex]\( C_3H_2(OH)_2 \)[/tex]
(iv) None of the above
#### Solution:
To verify the correct molecular formula, we must match the structural formula with the correct option:
- [tex]\( C_3H_6(OH)_2 \)[/tex]: This implies the molecule has 3 carbon atoms, 6 hydrogen atoms, and 2 hydroxyl groups (-OH).
- [tex]\( C_3H_5(OH)_3 \)[/tex]: This implies 3 carbon atoms, 5 hydrogen atoms, and 3 hydroxyl groups.
- [tex]\( C_3H_2(OH)_2 \)[/tex]: This implies 3 carbon atoms, 2 hydrogen atoms, and 2 hydroxyl groups.
Based on typical organic chemical structures, and without the actual structure being provided here, the most standard matching options would be:
(i) [tex]\( C_3H_6(OH)_2 \)[/tex]
### Question 4:
In the figure, the bee of condition B is converted to pupa in 5.5 days. Which type of honey bee can it form?
(i) Worker bee
(ii) Drone bee
(iii) Queen bee
(iv) Queen and worker bee
#### Solution:
- Worker bees are usually female and non-reproductive, with developmental periods generally ranging around 21 days.
- Drone bees are male and develop in about 24 days.
- Queen bees, which are reproductive females, develop in the shortest period, typically around 16 days.
Given that the bee in condition B is converted to a pupa in 5.5 days, this matches the developmental period typical for:
(iii) Queen bee
### Question 5:
When the mass of two bodies remains constant, and the distance between them is doubled, what will be the gravitational force exerted between them?
(i) [tex]\( F = G \frac{m_1 \cdot m_2}{d^2} \)[/tex]
(ii) [tex]\( F = G \frac{m_1 \cdot m_2}{2d^2} \)[/tex]
(iii) [tex]\( F = 2G \frac{m_1 \cdot m_2}{d^2} \)[/tex]
(iv) [tex]\( F = G \frac{m_1 \cdot m_2}{4d^2} \)[/tex]
#### Solution:
The gravitational force between two bodies is given by Newton's law of gravitation:
[tex]\[ F = G \frac{m_1 \cdot m_2}{d^2} \][/tex]
If the distance [tex]\( d \)[/tex] is doubled, the new distance becomes [tex]\( 2d \)[/tex]. The new force [tex]\( F_{\text{new}} \)[/tex] is:
[tex]\[ F_{\text{new}} = G \frac{m_1 \cdot m_2}{(2d)^2} = G \frac{m_1 \cdot m_2}{4d^2} \][/tex]
Therefore, the gravitational force becomes one-fourth of its original value:
(iv) [tex]\( F = G \frac{m_1 \cdot m_2}{4d^2} \)[/tex]
