Answer: A) 2 B) 4 C) 1
Explanation:
The electric field associated with a parallel-plate capacitor is defined as:
A) E=Q/(L^2 * ε0); if we double the charge, the resultant electric field becomes twice as strong as its initial value.
B) Referring to the earlier electric field expression, if the plate size is doubled, the final electric field will be a quarter of the original strength.
C) If the separation distance between the plates is increased twofold, the resulting electric field remains unchanged from its initial state.
Thermal Power is approximately 460W. According to the Stephan-Boltzmann Law Formula: P = єσT⁴A, where: P = radiation energy, σ = Stefan-Boltzmann Constant, T = absolute temperature in Kelvin, є = emissivity of the material, and A = the surface area. Given that σ = 5.67 x 10^(-8), ε = 0.6, and T = 30°C which converts to Kelvin as 303K, with the human body dimensions of 2m length and 0.8m circumference leading to an area of 1.6m², so thermal power equals 0.6 x 5.67 x 10^(-8) x 303⁴ x 1.6 = 458.8W. Rounding gives about 460W.
Answer:
Statements 4, 6 & 7 are incorrect.
Explanation:
In any elastic collision, the overall momentum vector sum of the system remains zero.
In this scenario, an elastic collision occurs between the ball and a stationary wall. The ball's velocity will consistently revert after the impact, leading to a change in direction of momentum.
The initial momentum of the ball is represented as:

where:
m = mass of the ball
v = initial velocity of the body
post-collision for the elastic interaction:

- Here, the momentum changes solely in direction, thus contradicting statement 7.
- During the impact, both the ball and the wall exert forces on each other that are equal and opposite. The wall remains motionless, while the ball is influenced by the wall's reaction force, performing work on it, which contradicts statement 4.
- Given that this collision is elastic, the ball's form and dimensions do not alter.
- The previous points clearly indicate that not all provided statements hold true, thus violating statement 6.
Explanation:
The formula for the electric field produced by an infinite sheet of charge is outlined below.
E =
where,
is the surface charge density
Following this, the formula for the electric force acting on a proton is given as:
F = eE
where, e is the charge of a proton
According to Newton's second law of motion, the overall force on the proton can be expressed as follows.
F = ma
a = 
= 
= 
According to kinematic equations, the proton's speed in the perpendicular direction can be described as follows.

= 
= 
= 683.974 m/s
Thus, the overall speed of the proton can be calculated as follows.
v' =
=

= 
= 1178.73 m/s
Consequently, we conclude that the proton's speed is 1178.73 m/s.
1. Independent variable: the variable that can be modified and regulated.
the nail polish on Sarah's nails
2. Dependent variable: outcomes that result from the changes in the independent variable.
the duration of the nail polish's longevity
3. <span> Hypothesis: Different brands of nail polish have varied durations before they chip.
</span> 4. Control group: the <span> independent variable remains unchanged in this setup, not subject to variations.
</span> the schedule of when Sarah applies her nail polish (Sarah colors her nails every Sunday for a month)
the specific base coat and top coat (she <span> applies the same bottom coat and top coat with every kind of nail polish)
weekly habits (she ensures the same routine each week so her nails are not treated more harshly on some weeks).
</span> Experimental group: <span> the independent variable is altered for this group
type of nail polish (Essie, OPI, and Sally Hansen)
</span> 6. Constants: the experimenter (Sally), duration of study (one week), her weekly routine, <span> base coat and top coat, </span>