Explanation:
The work done to lift the bag of weight mg through height 2.5 m is 400 J
The work done can be found by relation W = mg x h
Thus mg = [tex]\frac{W}{h}[/tex] = [tex]\frac{400}{2.5}[/tex] = 160 N
Therefore the man have to apply the force of 160 N
Answer:160newtons
Explanation:
Work=400J
Distance=2.5m
Time=2 seconds
Force=?
Force=work/distance
Force=400/2.5
Force=160
Force=160 newtons
21) A youngster having a mass of 50.0 kg steps off a 1.00 m high platform. If she keeps her legs fairly rigid and comes to rest in 10.0 ms, what is her momentum just as she hits the floor? What average force acts on her during the deceleration?
Answer:
-22,150 N
Explanation:
When the youngster jumps off the platform, during the fall her initial potential energy is converted into kinetic energy, according to the law of conservation of energy. Therefore, we can write:
[tex]mgh=\frac{1}{2}mu^2[/tex]
where the term on the left is the potential energy while the term on the right is the kinetic energy, and where
m = 50.0 kg is the mass of the youngster
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
h = 1.00 m is the heigth of the platform
u is the speed of the youngster as she reaches the floor
Solving for u,
[tex]u=\sqrt{2gh}=\sqrt{2(9.8)(1.00)}=4.43 m/s[/tex]
Then, when the youngster hits the floor, the force exerted on her during the deceleration is given by:
[tex]F=\frac{\Delta p}{\Delta t}=\frac{m(v-u)}{\Delta t}[/tex]
where [tex]\Delta p[/tex] is her change in momentum, and where
m is the mass
v = 0 is the final velocity (she comes to a stop)
u = 4.43 m/s is the initial velocity
[tex]\Delta t=10.0 ms =0.010 s[/tex] is the duration of the collision
Substituting,
[tex]F=\frac{(50.0)(0-4.43)}{0.010}=-22150 N[/tex]
And the negative sign means the direction of the force is opposite to the motion (so, upward).
How many dwarf planets are there in the solar system
Answer: 5
Explanation: There are 5 recognized dwarf planets in our solar system; Ceres, Pluto, Haumea, Makemake and Eris.
Answer:
5
Explanation:
There are only 5 dwarf planets that are officially recognized and they are Ceres, Pluto, Haumea, Makemake and Eris.
A youngster having a mass of 50.0 kg steps off a 1.00 m high platform. If she keeps her legs fairly rigid and comes to rest in 10.0 ms, what is her momentum just as she hits the floor? What average force acts on her during the deceleration?
The youngster's momentum just before hitting the floor is -500 kg*m/s, and the average force acting on her during deceleration is 25,000 N.
Explanation:To calculate momentum before hitting the floor, we use the formula: momentum = mass × velocity. Given the mass (m) as 50.0 kg and the height (h) as 1.00 m, we can find the initial velocity (v) using the equation for gravitational potential energy (PE = mgh) and converting it into kinetic energy (KE = 1/2mv^2). Solving for velocity, we get v = √(2gh) = √(2 × 9.81 m/s^2 × 1.00 m) ≈ 4.43 m/s.
Momentum = mass × velocity = 50.0 kg × 4.43 m/s = 221.5 kg*m/s. As she comes to rest, the change in momentum is Δp = final momentum - initial momentum = 0 - 221.5 kg*m/s = -221.5 kg*m/s. However, as the motion direction changes, the momentum also changes direction, so we take -221.5 kg*m/s as the momentum just before hitting the floor.
The average force during deceleration can be found using the impulse-momentum theorem, which states that impulse (change in momentum) is equal to force × time. Impulse = Δp = force × time. Rearranging the formula to solve for force, we get force = Δp / time. Substituting the values, force = -221.5 kg*m/s / (10.0 ms) = -22,150 N.
However, force is a vector quantity, and its direction opposes the motion, so the magnitude of the force is 22,150 N. As the force acts over 10.0 ms, the average force is 22,150 N / 10.0 ms = 25,000 N. Thus, the average force exerted on the youngster during deceleration is 25,000 N, with the negative sign indicating it opposes the motion.
Jimmy has two options for moving a piano up to the second floor of a hotel, which is 10 m above his current position. He can push the piano up 50 m ramp or lift the piano up with a rope wrapped around a pulley. Which option will require him to exert a greater average force? Neglecting friction, which option will require more work?
Answer:
Lifting straight up, even with a rope and pulley, always takes more force than going up a slanted ramp to the same height.
But if you use the ramp, then you have to exert the force over a greater distance (pull more rope to lift to the same height).
Astonishingly, the product of (force) x (distance) is the same number either way. So without friction, the total amount of work required is the SAME whichever way the piano is lifted.
What are the answer for the blanks
Which products rely on the ability of ionic compounds to conduct electricity?
Cell phones and remote control toys are the products which rely on the ability of ionic compounds to conduct electricity.
Explanation:
Ionic compounds are those which are formed between electronegative and electropositive elements. So some of the electrons will be always free in these compounds. Among the options given in the question, cell phones and remote control toys are the products which uses ionic products. As most of the semiconducting compounds or electronic compounds are ionic in nature. And cell phones and remote control toys uses the movement of electrons from ionic compounds to do the work.
Thus, cell phones and remote control toys are the products which rely on the ability of ionic compounds to conduct electricity.
Answer:
(B) cell phones
Explanation:
jus took the quiz
Alice builds an electric motor by positioning an electromagnet between the poles of a permanent magnet. When the electromagnet turns, the current through it switches direction because its connections to the voltage source are reversed. The repeated switching of the electromagnet's poles causes it to spin. This particular motor is used to turn the wheels of a toy car.
Which of the following actions would increase the amount of force applied to the wheels of the toy car?
A.
replacing the magnet with a stronger magnet
B.
increasing the distance between the magnet's poles and the electromagnet
C.
decreasing the number of loops in the electromagnet's coil
D.
decreasing the electric current running through the electromagnet
Answer:
A. replacing the magnet with a stronger magnet
Explanation:
In order to increase the force on the wheels, Alice needs to increase the force acting between the magnet and the electromagnet. There are several ways that she could do this:
replace the magnet with stronger magnet
increase the number of loops in the electromagnet's coil
increase the electric current running through the electromagnet
decrease the distance between the magnet's poles and the electromagnet
At 15°C air is transmitted
at 340 m/s. Express this speed
in Kilometers per hour.
Answer:
1224km/hr
Explanation:
To convert from m/s to km/hr
1000m = 1km
Divide both sides by 1000
1m = 1/1000 km................. (1)
60×60 seconds = 1 hr
3600s = 1hr
Divide both sides by 3600
1s = 1/3600 .............(2)
Divide (2) by (1)
1m/s = 1/1000 ÷ 1/3600 km/hr
1m/s = 1/1000 × 3600/1 km/hr
1m/s = 3600/1000 km/hr
1m/s = 3.6 km/hr .............(3)
To convert 340m/s to km/hr
Multiply (3) by 340
1× 340m/s = 3.6 × 340 km/hr
340m/s = 1224km/hr
I hope this was helpful, please mark as brainliest
Answer:
1224 km/hr
Explanation:
Method 1to convert m/s to km/hrrecall that :
1km = 1000m
firstly lets convert m to km
340 m to km
340 / 1000
= 0.34 km
recall that :
1hr = 60 min
1 min = 60 seconds
hence 1 hr = 60*60
1 hr = 3600 seconds
now to convert seconds to hr :1 second / 3600
=1/3600 hours
hence to get the answer you say :
[tex]\frac{0.34}{\frac{1}{3600} }[/tex]
= 1224 Method 2recall : 1km = 1000m
recall: 1hr = 60 min
1 min = 60 seconds
hence 1 hr = 60*60
1 hr = 3600 seconds
now to get this answer you have to divide m by 1000 to get km
and you have to divide seconds by 3600 to get hours
= [tex]\frac{340 / 1000}{1/3600}[/tex]
= 1224When a train first starts going down the railroad, it is very difficult for it to get going. When it comes to a stop, it has a hard time slowing down. Why is this?
A: balanced forces
B: unbalanced forces
C: inertia
Explanation:
When we apply the force on any body , the inertia comes into play . It is the tenancy of the the body to oppose the force which tends to change its state .
In first case the train tries to change its state from rest to motion . Thus the inertia of rest opposes this tendency.
In the second case , the train tries to come from motion to the state of rest . Thus again , inertia opposes it .
Therefore inertia is the factor which creates difficulty in both case . Hence option ( c ) is correct
Select all the correct answers.
Which three statements about electromagnetic radiation are true?
0
Light is a kind of electromagnetic radiation.
0
Electromagnetic radiation can travel only short distances.
O
Electromagnetic radiation has no mass.
O
Electromagnetic radiation can travel through a vacuum.
All kinds of electromagnetic radiation are invisible.
Yo sup??
the 1st, 3rs and 4th statement are true because electromagnetic waves can travel large distances and electromagnetic waves are visible (only 400-700 nm wavelenght)
Hope this helps
A hydraulic lift is used to lift a heavy box that is pushing down on a 1.5-m2 piston with a force of 1,700 N. What force needs to be exerted on a 0.12-m2 piston to lift the box?
Answer:
136 N
Explanation:
Pressure on large piston = pressure on small piston
F₁ / A₁ = F₂ / A₂
1700 N / 1.5 m² = F / 0.12 m²
F = 136 N
1. If a model train car with a momentum of 12 kg•m/s collides with a 2 kg model train car that is not moving, what is the total momentum of both cars after the collision?
Answer:
[tex]P_{f} = 12 \ kg.m/s[/tex]
Explanation:
Given data:
Momentum of moving model train, [tex]P_{1} = 12 \ kg.m/s[/tex]
Mass of the stationary model train, [tex]m = 2 \ kg[/tex]
Initial speed of the stationary model train, [tex]v = 0[/tex]
Assume there is no external force is acting on the given train system.
In this case, the total linear momentum of the trains would be conserved.
Let the final linear momentum of the trains be [tex]P_{f}.[/tex]
Thus,
[tex]P_{i} = P_{f}[/tex]
[tex]P_{1} + P_{2} = P_{f}[/tex]
[tex]P_{1} + mv = P_{f}[/tex]
[tex]12 + 2 \times 0 = P_{f}[/tex]
[tex]\Rightarrow \ P_{f} = 12 \ kg.m/s.[/tex]
The total momentum of both cars after the collision is 12 kg•m/s.
Explanation:The momentum of an object is the product of its mass and velocity. In this case, the initial momentum of the moving model train car is 12 kg•m/s while the other car is stationary, so its initial momentum is 0 kg•m/s.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the total momentum of both cars after the collision is 12 kg•m/s.
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Please Answer this....
Class 10 science board cbse 2020
Qn. 29
a) See attachment
b) -180 cm, virtual image
c) Magnification: 10, image is 10 times the size of the object, upright
Explanation:
a)
The ray diagram for this situation is shown in attachment.
In order to find the position of the image, we proceed as follows:
- We draw a ray of light going from the tip of the object towards the lens, parallel to the principal axis - this ray is refracted towards the principal focus on the other side
- We draw another ray of light going from the tip of the object towards the centre of the lens
- We prolong both rays: we see that they don't meet on the right side of the lens. Therefore, we prolong them on the left side, where they meet - this means that the image is virtual, because it cannot be projected on a real screen (it is formed on the same side as the object).
b)
To find the nature and the position of the image, we use the lens equation:
[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]
where:
f is the focal length
p is the distance of the object from the lens
q is the distance of the image from the lens
In this problem:
[tex]f=20 cm[/tex] is the focal length
[tex]p=18 cm[/tex] is the object distance
Solving for q, we find the position of the image:
[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{20}-\frac{1}{18}=-0.00555 cm^{-1}\\q=\frac{1}{-0.00555}=-180 cm[/tex]
The negative sign indicates that the image is virtual (on the same side of the object).
c)
The magnification is given by:
[tex]M=-\frac{q}{p}[/tex]
where
q is the image distance from the lens
p is the object distance from the lens
Here we have
[tex]q=-180 cm[/tex]
[tex]p=18 cm[/tex]
So the magnification is:
[tex]M=-\frac{-180}{18}=10[/tex]
This means that the image size is a factor 10 times the object size. In fact, we can write
[tex]y'=My[/tex]
where
y' is the image size
y is the object size
Substituting,
[tex]y'=10y[/tex]
So, the image is 10 times the object (in size), and it has the same orientation, upright (because of the positive sign).
A circuit has a voltage drop of 24.0 V across a 30.0 resistor that carries a
current of 0.800 A. What is the power conducted by the resistor? Use P = VI.
O A. 19.2 W
O B. 1.25 W
O c. 24.0 W
O
D. 720.0 W
(A) 19.2 W
Explanation:
Given-
Voltage drop, V = 24 V
Resistor = 30Ω
Current, I = 0.8 A
Power, P = ?
We know,
P = VI
P = 24 (0.8)
P = 19.2 W
Therefore, the power conducted by the resistor is 19.2 W
Answer:
19.2
Explanation:
Through which of the following can sound energy NOT be transferred?
Answer:
Vacuum
Explanation:
Sound energy as mechanical wave cannot be transmitted through a vacuum.
As a wave, which is a disturbance that transmits energy from one point to another, it requires a material medium for propagation.
Sound energy is a mechanical wave. It requires particles and a medium to be propagated. By so doing, this form of energy cannot be transmitted through a vacuum body. In such bodies, there is no medium of propagation.A wave with a frequency of 17 Hz has a wavelength of 4 meters. At what speed (in m/s) will this wave travel?
Answer:68m/s
Explanation:
Frequency=17Hz
Wavelength=4metre
Wave speed=frequency x wavelength
Wave speed =17 x 4
Wave speed =68m/s
How does secondhand smoke affect children?
It increases their asthma rates.
It increases their attention span.
It increases their learning ability.
It increases their chance of obesity.
Answer:
It increases asthma rates
Explanation:
Charles' Law
4. A gas has a volume of 4 liters at 50 °C. What will its volume be in liters) at 100°C?
Therefore, the volume of the gas at temperature 100°C is 4.62L
Explanation:
Given-
Volume, V1 = 4L
Temperature, T1 = 50°C = 50 + 273K = 323K
Temperature, T2 = 100°C = 100 + 273K = 373K
Volume, V2 = ?
Using Charles law:
V1/T1 = V2/T2
4/323 = V2/373
V2 = 4.62L
Therefore, the volume of the gas at temperature 100°C is 4.62L
The force needed to lift an object is equal in size to the gravitational force on the object. How much work is done in lifting an object that has a mass of 5 kg a vertical distance of 2 m?
Answer:
Work done in lifting the object = 98 J
Explanation:
Work: Work can be defined as the product of force and distance.
The S.I unit of work is Joules (J).
Mathematically it can be expressed as
W = F × d................. Equation 1
Where W = work done, F = force needed to lift the object, d = distance
The gravitational force on the object = Weight of the object
Weight of the object = mg .................. Equation 2
Where m = mass of the object, g = acceleration due to gravity
Given: m = 5 kg,
Constant: g = 9.8 m/s²
Substituting these values into equation 2
Weight of the object = 5 × 9.8
Weight of the object = 49 N
Since weight of the object = force needed to lift the object,
F = 49 N
Also Given: d = 2 m
Substituting these values into equation 1
W = 49 × 2
W = 98 J
Work done in lifting the object = 98 J
hope this helps
plz can i get brainliest:)
Monochromatic radiation of frequency greater than the threshold frequency is incident on a metal do all the electrons emitted by photoelectric emission have the same kinetic energy.
Yo sup??
No it isn't necessary that they will have the same Kinetic energy.
Hope this helps
I need help, Ill glady appreciate any responses
I know I am a smart person, but my doubtness does not let me
How can I start believing more on myself?
How can I be more confident?
Answer: Answer: First, You should try to think positive thoughts. Then, you should try and pinpoint your achievements. You often see your failures more than the success. Moreover, you should go check the impostor syndrome in ted ed. If you are trying to be more confident in your school choices than you should try to check the information again or try to go back and remember the time you studied the subject assignments you are doing.
Explanation: That other guy gave a great answer but can you still give a brainliest?
A 30 kg child climbs 15 meters up a tree. When he looks around, when is the child’s potential energy ?
Answer:
Gravitational potential energy of the child = 4410 J.
Explanation:
Given data:
Mass of the child, [tex]m = 30 \ kg[/tex]
Mass of the child, [tex]h = 15 \ m[/tex]
The gravitational potential energy of the child at 15 m height can be given as,
[tex]GPE = mgh[/tex]
[tex]GPE = 30 \times 9.80 \times 15[/tex]
[tex]GPE = 4410 \ \rm J.[/tex]
The potential energy of the child is 4410J
POTENTIAL ENERGY:
The potential energy (P.E) of a body refers to its energy at a position. The potential energy can be calculated using the formula below:P.E = mass (m) × gravitational force of the Earth (g) × height (h)
Where; g = 9.8m/s²
According to this question, a 30 kg child climbs 15 meters up a tree, his potential energy can be calculated thus:P.E = 30kg × 15m × 9.8m/s²
P.E = 4410Joules.
Therefore, the potential energy of the child is 4410J.Learn more at: https://brainly.com/question/24284560?referrer=searchResults
2. What is the speed (v) of a wave that has a wavelength (a)
of 2 m and a frequency (f) of 6 Hz?
Answer:12m/s
Explanation:
Frequency=6Hz
Wavelength=2m
Wave speed=frequency x Wavelength
Wave speed=6 x 2
Wave speed=12m/s
The speed of a wave with a frequency of 6 Hz and a wavelength of 2 m is 12 m/s.
Explanation:The speed (v) of a wave is calculated by the formula v = fλ, where 'f' is the frequency and 'λ' (lambda) is the wavelength. Given the frequency (f) of 6 Hz and a wavelength ('λ') of 2 m, we can compute the speed of the wave using this formula:
v = 6 Hz × 2 m = 12 m/s.
Therefore, the speed of the wave is 12 meters per second (12 m/s).
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Three resistors with values of 4.0 W, 6.0 W, and 8.0 W, respectively, are connected in series. What
is their equivalent resistance?
The answer would be 18 W
The equivalent resistance of three resistors with values of 4.0 ohms, 6.0 ohms, and 8.0 ohms connected in series is 18.0 ohms.
The question asks for the equivalent resistance of three resistors connected in series with resistance values of 4.0 ohms, 6.0 ohms, and 8.0 ohms. When resistors are connected in series, the equivalent resistance (Requiv) is the sum of the individual resistances. The formula used is Requiv = R1 + R2 + R3.
Applying the given values:
Requiv = 4.0 Ω + 6.0 Ω + 8.0 Ω
Requiv = 18.0 Ω.
Therefore, the equivalent resistance of the three resistors connected in series is 18.0 ohms.
What is the oscillation period of your eardrum when you are listening to the A4 note on a piano (frequency 440 Hz)?
The period is the inverse of the frequence:
[tex]T=\dfrac{1}{f}=\dfrac{1}{440}=0.0022\overline{72}[/tex]
Answer:
T = 0.002 s.
Explanation:
Given data:
Frequency, [tex]f = 440 \ \rm Hz[/tex]
The time period of oscillation of the eardrum can be expressed as,
[tex]T = \frac{1}{f}[/tex]
[tex]T = \frac{1}{440 \ \rm Hz}[/tex]
[tex]T = 0.002 \ s.[/tex]
Select the correct answer.
Which statement best explains that sound waves are pressure waves?
A.
Sound waves have regions of compressions and rarefactions.
B. Sound waves cannot propagate through metals.
C. Sound waves move perpendicular to the medium particles.
D. Sound waves cannot propagate through water.
Answer:
C
Explanation:
Sound waves move perpendicular to the medium particles.
Answer:
its c for sure
Explanation:
a heavy object falls with the acceleration as a light object during free fall. why?
A heavy object falls with the acceleration as a light object during free fall because:
Heavy things have a large gravitational force and also have less acceleration. So both the effects exactly cancel and make the falling objects to have the same acceleration irrespective of mass.
Free fall is a unique motion which has only gravitational force that acts on an object. Objects that undergo free fall experience only have the influence of gravity and not any other force.
So when we apply newton's second law of gravity which is:
[tex]\text {acceleration}=\frac{\text {Force}}{\text {mass}}[/tex]
where,
F is the force
m is the mass
a is the acceleration
For example: When a 1000 kg elephant and a 1 kg rat fall from the same height,
The acceleration can be calculated as follows:
For elephant: F = 10000 N and m = 1000 kg. So,
[tex]\text {acceleration}=\frac{10000}{1000}=10\ \mathrm{m} / \mathrm{s}^{2}[/tex]
For rat : F = 10 N and m = 1 kg
Thus, [tex]\text {acceleration}=\frac{10}{1}=1\ \mathrm{m} / \mathrm{s}^{2}[/tex]
Hence, it shows that both the animals have the same acceleration irrespective of their mass.
6. Water flows through a 9,6-cm-diameter fire hose with a speed of 1.3 m/s. At the end of
the hose, the water flows out through a nozzle whose diameter is 2.5 cm. What is the
speed of water coming out of the nozzle?
A) 4.99cm/s
B) 0.339m/s
C) 0.088m/s
D) 19.2m/s
Can someone please answer this question
Answer:
D) 19.2 m/s
Explanation:
We can solve this problem by using the continuity equation: in fact, the flow rate a fluid through a pipe must remain constant.
Therefore, we can write:
[tex]A_1 v_1 = A_2 v_2[/tex]
where
[tex]A_1[/tex] is the cross-sectional area of the 1st section of the pipe
[tex]A_2[/tex] is the cross-sectional area of the 2nd section of the pipe
[tex]v_1[/tex] is the velocity of the water in section 1
[tex]v_2[/tex] is the velocity of the water in section 2
For the pipe in the problem we have:
[tex]d_1=9.6 cm = 0.096 m[/tex] is the diameter of the hose, so the area is
[tex]A_1=\pi (\frac{d_1}{2})^2[/tex]
[tex]d_2=2.5 cm = 0.025 m[/tex] is the diameter of the nozzle, so the area is
[tex]A_2=\pi (\frac{d_2}{2})^2[/tex]
[tex]v_1=1.3 m/s[/tex] is the velocity of water in the hose
Solving the equation for v2, we find the speed of water in the nozzle:
[tex]v_2=v_1\frac{A_1}{A_2}=v_1 \frac{d_1^2}{d_2^2}=(1.3)\frac{(0.096)^2}{(0.025)^2}=19.2 m/s[/tex]
011 10.0 points
A sound wave has a frequency of 798 Hz in air
and a wavelength of 0.48 m.
What is the temperature of the air? As-
sume the velocity of sound at 0°C is 329 m/s.
Answer in units of °C.
vil
Explanation:
From the Newton's velocity of sound relationship , the velocity of sound is directly proportional to the square root of temperature .
In this case The velocity of sound = frequency x wavelength
= 798 x 0.48 = 383 m/sec
Suppose the temperature at this time = T K
Thus 383 ∝ [tex]\sqrt{T}[/tex] I
The velocity of sound is 329 m/s at 273 K ( given )
Thus 329 ∝ [tex]\sqrt{273}[/tex] II
Dividing I by II , we have
[tex]\frac{383}{329}[/tex] = [tex]\sqrt{\frac{T}{273} }[/tex]
or [tex]\frac{T}{273}[/tex] = 1.25
and T = 339.8 K = 66.8° C
A pendulum consisting of a sphere suspended from a light string is oscillating with a small angle with respect to
the vertical. The sphere is then replaced with a new sphere of the same size but greater density and is set into
oscillation with the same angle. How do the period and maximum acceleration of the new pendulum compare to
those of the original?
Period
Acceleration
a. Larger
Smaller
b. Smaller
Larger
C. The same
The same
d. The same
Smaller
Answer:
Explanation:
The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”.
The period of simple pendulum is given as
T=2π√l/g
Increasing the density of the object implies that the mass has increased
Because density is mass/volume
The period is independent on the density of the object, it depends on the length of the string and the acceleration due to gravity. So the period remains the same.
2. Acceleration
The acceleration of a simple pendulum is given as
a=-gSin θ
Therefore the acceleration is independent on the density of the object, it depends on the acceleration due to gravity and the angle of displacement.
Then, the acceleration remains the same.
So the answer is Option C,
Same
Same
Final answer:
Replacing a sphere with another of greater density in a pendulum, without changing the oscillation angle, does not affect the pendulum's period or maximum acceleration. Both remain the same because they are independent of the pendulum bob's mass or density.
Explanation:
The period of a pendulum is given by the formula T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. This formula shows that the period is independent of the mass or density of the pendulum bob. Hence, replacing a sphere in a pendulum with another sphere of greater density but the same size, and oscillating both at the same angle, does not change the period of the pendulum's oscillation. The maximum acceleration of a pendulum occurs at its lowest point and is given by a = g√(sinθ), where θ is the oscillation angle. Since the acceleration depends only on gravity and the angle of oscillation, which remain constant, the maximum acceleration of the pendulum will also remain the same irrespective of the mass or density of the bob.