37. which of the following expressions represents escape velocity?
a. $\frac{2gm}{r^2}$
b. $\sqrt{\frac{2gm}{r^2}}$
c. $\sqrt{\frac{2gm}{r}}$
d. $\frac{2gm^2}{r^2}$

38. which of the following observations occurs when a glass rod is rubbed with silk?
a. electrons from the glass are transferred to the silk.
b. protons from the glass are transferred to the silk.
c. electrons from the silk are transferred to the glass.
d. protons from the silk are transferred to the glass.

39. two point charges of 1.0 μc and 1.5 μc are 5.0 cm apart. calculate the magnitude of the force between them. ($\frac{1}{4\pi\epsilon_0} = 9.0 \times 10^9 \, \text{n m}^2 \text{c}^{-2}$)
a. 2.7 n
b. 5.4 n
c. 6.7 n
d. 7.0 n

40. two parallel plates separated by 15.0 mm have a potential difference of 2.0 kv between them. calculate the electric field intensity between the plates.
a. $1.3 \times 10^3 \, \text{n c}^{-1}$
b. $3.0 \times 10^4 \, \text{n c}^{-1}$
c. $7.5 \times 10^3 \, \text{n c}^{-1}$
d. $4.5 \times 10^4 \, \text{n c}^{-1}$

41. circuit diagram: 2ω, 6v, e=4v, 6ω. nodes d, c, a, b. currents $i_1$, $i_2$
using kirchhoff’s first law for electrical circuits, the current in the 6 ω resistor in the diagram above will be
a. $i_1 + i_2$
b. $i_1 - i_2$
c. $2i_1$
d. $i_2$

42. four lamps labelled p(110 v, 100 w), q(240 v, 60 w), r(250 v, 40 w) and s(300 v, 25 w) are switched on for the same duration. which of the lamps consumes the highest amount of electrical energy?
a. p
b. q
c. r
d. s

Question

37. which of the following expressions represents escape velocity?
a. $\frac{2gm}{r^2}$
b. $\sqrt{\frac{2gm}{r^2}}$
c. $\sqrt{\frac{2gm}{r}}$
d. $\frac{2gm^2}{r^2}$

38. which of the following observations occurs when a glass rod is rubbed with silk?
a. electrons from the glass are transferred to the silk.
b. protons from the glass are transferred to the silk.
c. electrons from the silk are transferred to the glass.
d. protons from the silk are transferred to the glass.

39. two point charges of 1.0 μc and 1.5 μc are 5.0 cm apart. calculate the magnitude of the force between them. ($\frac{1}{4\pi\epsilon_0} = 9.0 \times 10^9 \, \text{n m}^2 \text{c}^{-2}$)
a. 2.7 n
b. 5.4 n
c. 6.7 n
d. 7.0 n

40. two parallel plates separated by 15.0 mm have a potential difference of 2.0 kv between them. calculate the electric field intensity between the plates.
a. $1.3 \times 10^3 \, \text{n c}^{-1}$
b. $3.0 \times 10^4 \, \text{n c}^{-1}$
c. $7.5 \times 10^3 \, \text{n c}^{-1}$
d. $4.5 \times 10^4 \, \text{n c}^{-1}$

41. circuit diagram: 2ω, 6v, e=4v, 6ω. nodes d, c, a, b. currents $i_1$, $i_2$
using kirchhoff’s first law for electrical circuits, the current in the 6 ω resistor in the diagram above will be
a. $i_1 + i_2$
b. $i_1 - i_2$
c. $2i_1$
d. $i_2$

42. four lamps labelled p(110 v, 100 w), q(240 v, 60 w), r(250 v, 40 w) and s(300 v, 25 w) are switched on for the same duration. which of the lamps consumes the highest amount of electrical energy?
a. p
b. q
c. r
d. s

Accepted Answer

### Question 37
# Explanation:
## Step1: Recall escape velocity formula
The formula for escape velocity $ v_e $ is derived from equating gravitational potential energy to kinetic energy. The formula is $ v_e = \sqrt{\frac{2GM}{R}} $, where $ G $ is the gravitational constant, $ M $ is the mass of the celestial body, and $ R $ is its radius.
## Step2: Match with options
Looking at the options, option C is $ \sqrt{\frac{2GM}{R}} $, which matches the escape velocity formula.
# Answer: C. $ \sqrt{\frac{2GM}{R}} $

### Question 38
# Brief Explanations:
When a glass rod is rubbed with silk, glass has a tendency to lose electrons (since it is less electronegative than silk). So electrons from the glass are transferred to the silk. Protons are bound in the nucleus and do not transfer during charging by friction.
# Answer: A. Electrons from the glass are transferred to the silk.

### Question 39
# Explanation:
## Step1: Recall Coulomb's Law
Coulomb's Law is $ F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} $, where $ \frac{1}{4\pi\epsilon_0}=9.0\times 10^{9}\ Nm^2C^{-2} $, $ q_1 = 1.0\ \mu C=1.0\times 10^{-6}\ C $, $ q_2 = 1.5\ \mu C = 1.5\times 10^{-6}\ C $, and $ r = 5.0\ cm=0.05\ m $.
## Step2: Substitute values into the formula
$$
\begin{align*}
F&=9.0\times 10^{9}\times\frac{(1.0\times 10^{-6})\times(1.5\times 10^{-6})}{(0.05)^2}\
&=9.0\times 10^{9}\times\frac{1.5\times 10^{-12}}{0.0025}\
&=9.0\times 10^{9}\times6\times 10^{-10}\
&= 5.4\ N
\end{align*}
$$
# Answer: B. 5.4 N

### Question 40
# Explanation:
## Step1: Recall electric field and potential difference relation
The electric field $ E $ between two parallel plates is given by $ E=\frac{V}{d} $, where $ V $ is the potential difference and $ d $ is the distance between the plates.
## Step2: Convert units
$ V = 2.0\ kV=2000\ V $, $ d = 15.0\ mm = 0.015\ m $
## Step3: Calculate $ E $
$$
E=\frac{2000}{0.015}\approx1.3\times 10^{5}\ N/C
$$
# Answer: A. $ 1.3\times 10^{5}\ N\ C^{-1} $

### Question 41
# Brief Explanations:
Kirchhoff's first law (current law) states that the sum of currents entering a junction is equal to the sum of currents leaving a junction. In the diagram, at junction D (or C), the current through the 6$\Omega$ resistor (let's say $ i $) should be equal to $ i_1 + i_2 $ if we consider the directions. Wait, actually, looking at the circuit: the two batteries and resistors. The current in the 6$\Omega$ resistor: let's see the junctions. The current $ i_1 $ is through 2$\Omega$, $ i_2 $ is through the 4V battery branch, and the current through 6$\Omega$ should be $ i_1 + i_2 $ (depending on the direction, but the option A is $ i_1 + i_2 $).
# Answer: A. $ i_1 + i_2 $

### Question 42
# Explanation:
## Step1: Recall electrical energy formula
Electrical energy $ E = Pt $, where $ P $ is power and $ t $ is time. Since $ t $ is the same for all lamps, the lamp with the highest power $ P $ will consume the most energy.
## Step2: Compare powers
The powers of the lamps are: P: 100 W, Q: 60 W, R: 40 W, S: 25 W. So P has the highest power.
# Answer: A. P

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QUESTION IMAGE

Question

Explanation:

Question 37

Step1: Recall escape velocity formula

Step2: Match with options

Step1: Recall Coulomb's Law

Step2: Substitute values into the formula

Answer:

Question 38