If the length of the pendulum in pendulum clock increases by 0.1 % , then the error in time per day is
a) 86.4s
b) 4.32s
c) 43.2s
d) 8.64s
JEE Mains 2022
When the length of the pendulum in pendulum clock increases by 0.1 % , then the error in time per day is c) 43.2s
How to calculate the time?Let the pendulum = L
The time in a day will be: = 60 × 60 × 24
When the length is increased, the new length will be:
= L + 0.001L
New time period will be:
T =✓0.001s
Now, the error in a day will be:
= ✓0.001 × 60 × 60 × 24 - 1 × 60 × 60 × 24.
= 60 × 60 × 24(✓1.001 - 1)
= 43.2 seconds.
Therefore, the correct option is C.
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What distance has a car driven if it starts from rest and accelerates at a constant rate of 20 m/s/s for 7 seconds?
The distance traveled in meters is 290m. It can be solved using Newton's Laws of motion.
You can solve this problem by using the formula of
d = 1/2 a t^2
where d is the distance traveled in meters,
a = 20 m/s², and t =7 seconds
Plug-in the data to the formula and solve for the distance traveled after
7 s.
d = 1/2 a t^2
=1/2 × 20 × 7²
= 290m
Hence the dist travelled by the car is 290m
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A dog running in an open field has components of velocity vx = 2.8 m/s and vy = -1.8 m/s at time t1 = 12.0 s. For the time interval from t1 = 12.0 s to t2 = 25.0 s, the average acceleration of the dog has magnitude 0.45 m/s2 and direction 36.0 ∘ measured from the +x-axis toward the +y-axis.
The x and y component of the dog's velocity at t₂ = 25.0 s is 7.53 m/s and 2.933 m/s respectively.
The magnitude of the dog's velocity is 8.076 m/s.
The velocity components of a dog running in an open field are:
[tex]v_{x}=2.8 {~}m/s\\v_{y}=-1.8{~}m/s[/tex] at t₁ = 12 sec.
The average acceleration of the dog in the time interval t₁ = 12 sec to t₂ = 25 sec is 0.45 m/s² and the direction 36°.
(A) The x component of the dog velocity at t₂ = 25 sec will be:
Vₓ = vₓ + aₓ(cos(36)) × (t)
Vₓ = 2.8 + ( 0.45) × (0.89) × ( 25 - 12 )
Vₓ = 2.8 + 4.7327
Vₓ = 7.53 m/s
(B) The y component of the dog's velocity at t₂ = 25 sec will be:
[tex]V_y=v_y+a_y(cos(\theta))t\\V_y=-1.8+(0.45)(cos(36))(25-12)\\V_y=-1.8+4.7327\\V_y=2.933{~}m/s[/tex]
(C) Therefore, the magnitude of the dog's velocity is:
[tex]V=\sqrt{(v_x)^{2}+(v_y)^{2}}\\V=\sqrt{(7.53)^{2}+(2.93)^{2}}\\ V=\sqrt{56.7+8.58}\\ V=\sqrt{65.28}\\ V=8.0796{~}m/s[/tex]
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The complete question is mentioned below:
A dog running in an open field has components of velocity vₓ = 2.8 m/s and [tex]v_y = -1.8{~} m/s[/tex] at time t₁ = 12.0 s. For the time interval from t₁ = 12.0 s to t₂ = 25.0 s, the average acceleration of the dog has a magnitude of 0.45 m/s² and a direction of 36.0° measured from the +x-axis toward the +y-axis.
(A) At time t₂ = 25.0 s, what is the x-component of the dog's velocity?
(B) At time t₂ = 25.0 s, what is the y-component of the dog's velocity?
(C) What is the magnitude of the dog's velocity?
The current flowing through a lamp is 1.5AIt is plugged into a 120 V outletWhat is the resistance of the lamp? Ω
Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.
What is the resistance of the lamp?Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.
V = IR
Where V is the voltage or potential difference, I is the current and R is the resistance.
Given the data in the question;
Current I = 1.5AVoltage V = 120VResistance R = ?Plug the given values into the equation above and solve for R.
V = IR
120 = 1.5 × R
R = 120/1.5
R = 80Ω
Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.
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Answer:
80 is the answer
Explanation:
If a ball is thrown upward at a speed of 10 m/s, and it reaches a height of 5.1 meters, how long
will it be in the air total?
Answer:
t = 10/9.81 = 1.02s
Explanation:
the ball will be up in the air for 1.02 seconds
4. A radiographic technique of 100mA at 1/4 s has been used. If one
changes to the 400 mA station, the appropriate exposure time for the
same mAs is:
awnser D. 1600 mA
Explanation:
Ns/Np=Ip/Is
current is inverse
100/800=200/x
100x=160000
x=1600
2.Three sets of temperatures in Celsius, Fahrenheit and Kelvin scales respectively are given below. In which set do the thermometer scales show temperature of the same object? (a) 0°C, 32° F, 273 K (b) 0° C, 60° F, 373 K (c) 10° C, 32° F, 373 K
What is water pollution
And they're causes in Florida
The description of water pollution and it's likely causes in Florida can be found below.
What is water pollution?Water pollution is the contamination of water, especially surface water, by sewage effluent, fertilizer runoff, industrial chemical discharge etc.
These contaminants are called pollutants and when released into a body of water can deteriorate water quality and hamper its usage by humans.
Water pollution in Florida or any other developed state/country of the world can be caused by the following:
spills or leaks from oil and chemical containers.waste effluent going into surface water drains removing too much water from surface waters and groundwater.run-off containing fertilisers and pesticides from farming into surface waters.Learn more about water pollution at: https://brainly.com/question/19920929
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A disc rotates about its axis at a constant rate. If the acceleration of the outer rim of the disc is 4.9 m/s2, and the period of the rotation is 2.0 s, what is the radius of the disc?
The radius of the disc will be 0.496 meters.
What is Angular velocity?The pace at which an object rotates or revolves around an axis is known as its angular velocity. The Greek letter omega stands for angular velocity. Because it is expressed as an angle per unit of time, angular velocity in the SI is measured in radians per second. [[tex]M^{0}L^{0}T^{-1}[/tex]] is the dimensional formula for angular velocity.
According to the question, the given values are :
Acceleration, a=4.9 m/s² and,
Period of rotation, T=2.0 seconds
So, angular velocity (ω) of disc =2π/T
⇒2π/2
= π rad/sec.
Acceleration= rω²
4.9= r×π²
r=0.496 meters.
Hence, the radius of the disc will be 0.496 meters.
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A car is traveling due north at 23.6 m>s.
Find the velocity of the car after 7.10 s if its
acceleration is (a) 1.30 m>s2 due north, or
(b) 1.15 m>s2 due south.
A car is traveling due north at 23.6 m>s.
Find the velocity of the car after 7.10 s if its
acceleration is
The acceleration is known to be: a(t) = 1.7 m/s2.
We must integrate over time to obtain the velocity function, and the results are:
v(t) = (1.7m/s^2)
*t + v0
If we suppose that we begin at 23.6 m/s, then the initial velocity is: v0 = 23.6 m/s, where v0 is the beginning velocity.
The velocity formula is then: v(t) = (1.7m/s2).
*t + 23.6 m/s
We now seek to determine the value of t such that v(t) = 27.8 m/s.
Consequently, v(t) = 27.8 m/s = (1.7 m/s2)
*t + 23.6 m/s = (1.7 m/s2) 27.8 m/s - 23.6 m/s
t = 2.5 seconds when *t 4.2 m/s = (1.7 m/s/2)
At such acceleration, 2.5 seconds are required.
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A car travels 1,139 meters South, and 37 seconds what is the average velocity in meters per second to the South?
Answer:
see below
Explanation:
1 139 m / 37 s = 30.784 m/s South
3. A cube of Brass (density = 8.74g/cm³) has a mass of 87.321 grams. Determine
the height of the cube in cm. And in inches (1.00in = 2.54cm)
A cube of brass is ((density = 8.74g/cm³) .The height of the cube after calculating the given details is 2.15443 cm.
WHAT IS DENSITY ?Due to differences in density, two identically sized cubes constructed of different materials will typically not weigh the same when compared when weighed. Additionally, it implies that a massive Styrofoam cube can have the same weight as a tiny lead cube. Platinum, lead, iron, and other dense materials are a few examples
CALCULATIONDensity = 8.74 g/cubic cm
mass = 87.321 gms
Density = mass / volume
volume = mass / density = 9.99096109 cubic cm ≈ 10 cubic cm
side of cube = ∛10 cm = 2.15443 cm
∴ height of cube = 2.15443 cm .
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A curve at a racetrack has a radius of 800 m and is banked at an angle of 7.0°. On a rainy day, the coefficient of friction between the cars' tires and the track is 0.50. What is the maximum speed at which a car could go around this curve without slipping?
The maximum speed at which a car could go around this curve without slipping is6.12m/s
To solve this it is necessary to take concepts related to Centripetal Force and Friction Force.
In the case of the centripetal force,
Fc = mv²/r ....1
Where,
m=mass
v= velocity
r= Radius
In the case of the Force of Friction we have to,
F= [tex]\mu[/tex]mg ......1.
Where,
[tex]\mu[/tex] = Friction Constant
m= mass
g= gravity
the centripetal equal to the friction force to stay on the road, in this way
mv²/r = [tex]\mu[/tex]mg
v² = mgr
v = √([tex]\mu[/tex]gr)
The coefficient of friction between the cars' tires and the track
[tex]\mu[/tex] = 0.50
radius = 800m
g = 9.8 m/s²
using above values we get
v = [tex]\sqrt[]{800*9.8*0.5}[/tex]
V = 6.12m/s
The maximum speed at which a car could go around this curve without slipping is6.12m/s
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11 )Four forces of magnitude 10 N, 5 N, 4 N and 6 N act on an object in the directions North, West, East, and South respectively. Find the magnitude and direction of their resultant.
The magnitude and direction of resultant force is 4.12N and direction is 75.96degree
The combined force that affects a body in a different way is known as the resultant force. Typically, it uses a vector calculation to calculate.
F net = / (square root of F1 resultant + F2 resultant + F1F2 cos tita)/........(1)
For instance, if two forces are acting in the same direction, we add them together; if they are acting in opposition, we subtract them from one another.
When two forces are exerting pressure on a body at an angle of, the combined net force is 4N in the direction of North. In this case, the two forces are 10N and 6N, which are operating in opposing directions. Additionally, 5N and 4N are moving in the other direction, resulting in a net force of 1N moving westward from these two forces.
by substituting we get F net =4.12N
direction is = 4 / tan tita = 75.96 degree
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Two batteries of 7 V and 13 V with the internal resistances 1 ohm and 2 ohm respectively are connected in parallel with a resistance of 12 22. Find the current through each branch of the circuit and the potential difference across 12 ohm resistance.
the current through each branch of the circuit and the potential difference across 12-ohm resistance is 0.711A
The flow of charge is the current. A component is used to measure current. Potential difference is measured between two points on either side of a component because it represents the energy transferred between two points in a circuit.
-12(I1+I2) -1I1+7=0
12(I1+I2) +1I1=7
For the loop
-12(I1+I2) -2I=13
From 1&2
2I -I1=13-7=6
I1=2I2-6
The crucial distinction between current and voltage. Current in the circuit flows due to voltage, which is the potential difference between two locations in an electric field. The term "current" refers to the rate at which electrons are moving.
I2=85/38=2.237A
I1=2I 2-6
I1=2 x 85/38-6=-1.526A
I=I1+I2=-1.526+2.237=0.711A
Potential difference across 12-ohm resistance
V=0.711 x 12=8.53 v
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Stone Bonner throws a football pass horizontally to his teammate. How could he
increase the range the ball covers during the throw?
There is nothing he could do to increase the range because gravity is constant.
He could throw the ball from a lower height.
He could choose a a football with less mass.
He could throw the ball with a greater horizontal velocity
He can increase the range of the ball covers during the throw by throwing the ball with a greater horizontal velocity
Assuming a projectile is launched from the ground level, the range is defined as the distance between the launch point and the point where the projectile hits the ground.
Range = [tex]u^{2}[/tex] sin (2 (theta )) / g
u = initial horizontal velocity
g= acceleration due to gravity
theta = angle of velocity vector with the ground
since , initial horizontal velocity is directly proportional to the range
hence , if we increase horizontal velocity range of the projectile will also increase .
hence , correct option is d) He could throw the ball with a greater horizontal velocity
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John Deere, a U.S. company, sells a tractor to a farmer in Canada what Gdp category is it in?
John Deere, a U.S. company, sells a tractor to a farmer in Canada. It is a GDP category is net exports.
Who is a farmer?Farmers are the person who usually cultivates and grows crops. They often also have cattle farming also. These farmers earn money by selling the crops in the market.
As a person is exporting goods and services to the US market, then we can say that the person is an exporter of court. There is GDP which is gross domestic product the US company that sells the status to Canada will be termed as the net exporter and represented over in that category.
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A pebble of mass 0.05kg is thrown vertically upwards. Give the direction and
magnitude of the net force on the pebble.
(a) During its upward motion.
(b) At the highest point where it is momentarily at rest.
In each case, 0.5N of force in a downward direction
No matter which way an object is moving, gravity's acceleration always works downward. In all three scenarios, the stone is just subject to the gravitational pull. According to Newton's second rule of motion, its magnitude is as follows:
Force=ma
Where, m is a mass of the pebble and a is acceleration due to gravity
F = Net force.
M = 0.05 kg of pebble mass
a=g=10m/s^2 F=0.05 × 10=0.5N
In all three scenarios, there is a downward-moving net force of 0.5N acting on the stone.
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Question 3 (1 point)
You are traveling up on an elevator to the 95th floor of the Hancock tower. As it
nears the 95th floor, your weight appears to be ?
You are traveling up on an elevator to the 95th floor of the Hancock tower. As it nears the 95th floor, your weight appears to be lighter.
Here is an exercise in thought. Consider a container with internally completely reflecting surfaces that is partially filled with light and located at sea level on Earth. The light will be somewhat gravitationally redshifted as it ascends, which will cause it to reflect at the top of the container with a little less momentum. Similar to how it will be blue shifted when travelling downward and give the container's bottom greater momentum. Weight is a quality of something that is subject to gravity. Light is drawn to objects with mass by gravity because it has energy. Since two photons (separate "pieces" of light, in a broad sense) have energy, I imagine they would be attracted to one another gravitationally. However, it would be really little.
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Consider the two vectors, A= 19.5x + 13.5y and B=3.4x - 4.5y.
What is the magnitude of the vector A - B?
What is the angle of the vector A - b, measured counterclockwise in degrees from the positive x-axis?
What is the magnitude of the vector 3A + B?
What is the angle of the vector 3A + B, measured counterclockwise in degrees from the positive x-axis?
The calculated angle is 305° and if v=a,b is the position vector, then |v|=a²+b² is the calculated magnitude.
If v=a,b is the position vector, then |v|=a²+b² will give the magnitude. Depending on the application, the direction is equal to the angle made with the x-axis or the y-axis. The formula tan=(ba)=tan1 determines the direction of a position vector (ba), We may say that the vector must be inclined in the fourth quadrant in this case because the vector's x and y components are both positive.
Consequently, the angle must be greater than 270 degrees and less than 360 degrees.
Now, in order to determine the value, we can say that
tanθ=opposite side/adjacent side
=8.6/6.1
=tan⁻¹1.41
=54.65, which indicates that it is inclined at an angle above with the X axis in the fourth quadrant (360-54.65 = 305.6°).
Consequently, the proper response will be 305° degrees if the angle is measured counterclockwise.
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4. A wave is described by the following equation: = 10i(40 − 2).
a) Identify the wavenumber and angular frequency and calculate the frequency, period, wavelength, and the speed of the wave. b) Draw the wave for t = 0.
The calculated answer is 320 cm/s.
The wave diagram is attached below.
The quantity of waves that pass a set location in a predetermined period of time is known as frequency. Therefore, if a wave passes through in half a second, the frequency is 2 per second. The frequency is 100 times per hour if it takes 1/100 of an hour. Even though the concept of frequency as it is commonly understood is based on events per second, other units of time, like minutes or hours, may also be employed.
For a wave with the equation y=Acos(kx)t,
k= 2 = 40cm² =0.157rad/cm,
v=28=50.3rad/s,
T= 1/ = 1/8Hz
=0.125s.
Wave speed = k = 0.157*50.3
= 320 cm/s
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Recording a change in which of the following would be an
example of a qualitative observation?
a velocity
b color
c force
d power
Chec
Recording a change in color would be an example of a qualitative observation and is therefore denoted as option B.
What is Qualitative observation?This is referred to as the type of observation which is characterized by the use of our senses such as sight, smell etc while on the other hand quantitative observation has to do with measurement of different types of number variables and parameters
Color was chosen as the most appropriate choice because it doesn't deal with numbers and it can be felt with the use of our sense of smell which is present in the nose of individuals.
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5. A ball is shot into the air with an unknown initial velocity. The ball reaches its highest point after 7 seconds, at which point it has traveled 40 meters into the air. What was its initial velocity?
When using
association to
store and
remember
information,
you are also
A. neural
networking
B. encoding
C. duplicating
When using association to store and remember information, you are also encoding.
When trying to store and remember information, the following stages take place in order:
EncodingStorageRetrievalStoring a memory trace is called as encoding. Perception leaves representation in memory. It is the conversion of information for storage purposes.
Therefore, when using association to store and remember information, you are also encoding.
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A coin is dropped from a height of {x} meters. Neglecting air resistance, how much
time (in seconds) was the coin in the air?
Please help
The time of motion of the coin is determined as t = √(0.204x).
What is time of motion of a projectile?
The time of motion of an object or a projectile is the time taken for the objects to travel from its initial position to the final position.
The time taken for the coin to fall from the given height "x" is calculated as follows;
h = vt + ¹/₂gt²
where;
h is the height from which the coin is dropped = xv is the initial vertical velocity of the coin = 0t is the time of motion of the coin g is acceleration due to gravity = 9.8 m/s²x = 0 + ¹/₂gt²
2x = gt²
t² = 2x/g
t = √(2x/g)
t = √(2x/9.8)
t = √(0.204x)
Thus, the time of motion of the coin is determined as t = √(0.204x)
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A 1900 kg car traveling at a speed of 14 m/s
skids to a halt on wet concrete where = 0.60.
How long are the skid marks?
The length of the skid marks is 136m.
Speed is the time charge at which an object is moving alongside a path, whilst pace is the price and direction of an item's movement. The rate of change of role of an item in any route. speed is measured because of the ratio of distance to the time in which the space changed into included.
calculation,
mass of car = 1900kg
speed = 14 m/s
F = ma
a = F(friction) / m
F(friction) = mu F(normal)
F(friction) = mu g m
a = mu g m / m
a = mu g
a = 0.6 * 9.81m/s²
a = 5.886 m/s²
v² = 2 a x
x = v² / 2 a
x = (40m/s)²/ 2 * 5.886m/s²
x = 136m
Speed is a way of measuring how quickly something is shifting or being executed, or something moving rapidly. Speed is described because of the charge of trade of distance with time. It has the dimension of distance by time. therefore, the SI unit of pace is given as the aggregate of the simple unit of distance and the primary unit of Time. for this reason, the SI unit of velocity is a meter in step 2d. the rate of a body is converting with appreciation to time it's far shifting with a non-uniform velocity.
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What is the neutralizing reaction, and why is neutralization important?
A neutralization reaction is when an acid and a base react to form water and a salt and involves the combination of H+ ions and OH- ions to generate water.
What is the direction of the velocity and
acceleration vectors of a baseball that is rising upward
towards its highest point above the ground?
Answer:
The direction of the velocity vector is upward and the direction of the acceleration vector is downward. A ball thrown straight upward moves initially with a decreasing upward velocity.
Explanation:
Interpreting Graphics
6. Figure 1.9 shows position-time graphs of the straight-line movement of
two brown bears in a wildlife preserve. Which bear has the greater aver-
age velocity over the entire period? Which bear has the greater velocity
at t = 8.0 min? Is the velocity of bear A always positive? Is the velocity of
bear B ever negative?
Answer:
Time difference = T1-T2 = D1/V1-D2/V2 = D ( 1/V1-1/V2)
Time difference = 5.5 min = 5.5*60=330 sec, V1 = .09 m/s, V2= 1.9 m/s
330 = D (1/.9 – 1/1.9)
330= D(1.11-.5263)
330=D(.585)
D= 330/.585 = 564.3 m
Explanation:
Ilya and Anya each can run at a speed of 7.50 mph and walk at a speed of 3.50 mph . They set off together on a route of length 5.00 miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.
- Find Anya's average speed. (express in miles per hour)
- How long does it take Ilya to cover the distance? (express in minutes)
- Now find Ilya's average speed. (express in miles per hour)
The correct answer is 54.6 min.
Running speed of Ilya and Anya is v_r=7.50 mi/hr
Walking speed of Ilya and Anya is v_w=3.50 mi/hr
Total length of the route is d=5.00 miles.
Total time taken by Anya to cover the distance is
[tex]t_A= d/2/v_r+ d/2/v_w[/tex]
[tex]t_A= d/2v_r + d/2v_w[/tex]
[tex]t_A=d/2 \times1/v_r +1/v_w[/tex]
[tex]t_A= d/2 \times v_r+v_w / v_rv_w[/tex]
[tex]t_A[/tex]= 5.00/2 × 7.50+3.50/7.50 × 3.50 hr
[tex]t_A[/tex]= 5.00/2 × 11/26.25 hr
[tex]t_A[/tex]= 55/52.5 hr
[tex]t_A[/tex]=1.05 hr
Therefore Anya will take 1.05 hr to cover the distance.
Average speed of Anya is
[tex]v_{avg} = d/t_A[/tex]
[tex]v_{avg}[/tex]= 5.00/1.05 mi/hr
[tex]v_{avg}[/tex] = 4.76 mi/hr
Therefore Anya's average speed is 4.76 mi/hr.
If total time taken by Ilya to cover the distance is t , then
([tex]v_r[/tex] × t/2+(v_w × t/2=d))
t/2 × ([tex]v_r+v_w[/tex])=d
t × ([tex]v_r+v_w[/tex])=2d
t = 2d/([tex]v_r+v_w[/tex])
t = 2 × 5.00/7.50+3.50
t = 10/11 hr
t = 0.91 × 60 min
t = 54.6 min
Therefore total time taken by Ilya to cover the distance is 54.6 min.
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