By equating the two forces, acceleration due to gravity g is obtained which is independent of mass
What is Newton’s Second Law ?The law state that the rate of change of momentum is directly proportional to the force applied.
From Newton’s Second Law, Force F = mg. And from Newton’s Law of Universal Gravitation, Force F = GMm/r²
Where m is the mass of the satellite or the body revolving round the earth.
Equate the two forces.
mg = GMm/r²
The two m cancelled out leaving
g = GM/r²
Where
g = Acceleration due to gravityM = Mass of the earthG = Universal gravitational constantr = Distance between them.Therefore, since the mass of the satellite m has cancelled out, acceleration due to gravity g is independent of mass.
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What is the mass of 12 m3 of methylated spirit whose relative density is 0.8 ? ( Hint the density of water = 1000 kgm-3 ) A. 9600 kg B.9400 kg C. 8600 kg
ANSWER
A. 9600 kg
EXPLANATION
Given:
• The volume of the substance, V = 12m³
,• The relative density of the substance, 0.8
,• The density of water, 1000 kg/m³
Unknown:
• The mass of the substance, m
The relative density of a substance is defined as,
[tex]\rho_{relative}=\frac{\rho_{substance}}{\rho_{water}}[/tex]And the density of a substance is,
[tex]\rho=\frac{m}{V}[/tex]Let's solve the first formula for the density of the substance,
[tex]\rho_{substance}=\rho_{relative}\cdot\rho_{water}=0.8\cdot1000\operatorname{kg}/m^3=800\operatorname{kg}/m^3[/tex]Then, solve the second formula for m,
[tex]m=\rho\cdot V=800\operatorname{kg}/m^3\cdot12m^3=9600\operatorname{kg}[/tex]Hence, the mass of this substance is 9600 kg
Given v = 145 sin (200πt + 3π/2), what is the period?Question 12 options:10 msec5 sec.03 sec.005 sec
For a sine or cosine function of the form:
[tex]A\sin (B(x+C))+D[/tex]the perfiod is given by:
[tex]\frac{2\pi}{B}[/tex]In this case we have that:
[tex]B=200\pi[/tex]Then we have:
[tex]\frac{2\pi}{200\pi}=\frac{1}{100}=0.01=10\times10^{-3}[/tex]Therefore, the period is 10 ms
How much time would it take a car to go from a speed of 10m/s to 30m/s if it acceleratesat a rate of 4.0m/s/s?
Given,
The initial velocity of the car, u=10 m/s
The final velocity of the car, v=30 m/s
The acceleration of the car, a= 4.0 m/s²
From one of the equations of the motion, we have
[tex]v=u+at[/tex]Where t is the time duration.
On rearranging the above equation,
[tex]t=\frac{v-u}{a}[/tex]On substituting the known values,
[tex]t=\frac{30-10}{4.0}=5\text{ s}[/tex]Therefore the time that the car takes to accelerate is 5 s
Two different masses have equal, non-zero kinetic energies. The momentum of the smaller mass isSelect one:A) smaller than the momentum of the larger mass.B) There is not enough information to answer the question.C) equal to the momentum of the larger mass.D) zero.E) Larger than momentum of the larger mass.
Let the mass of smaller object be m and mass of larger object be M.
As the kinetic energies are equal,
[tex]\frac{p_m^2}{2m}=\frac{p^2_{_M}}{2M}[/tex]On solving further,
[tex]\frac{p_m}{p_M}=\text{ }\sqrt[]{\frac{m}{M}}[/tex]Hence, option A is correct.
A 1 kg apple and a 2 kg grapefruit are 2 m apart. What is the force of gravity between each fruit?
According to Newton's law of gravitation, any particle of matter in the universe attracts any other with a force varying directly as the product of their masses and inversely as the square of the distance between them. It is expressed as
F = Gm1m2/r^2
where
G = gravitational constant and its value is G = 6.673 x 10^-11 Nm^2/kg^2
m1 and m2 are the masses of the bodies
r is the distance between the bodies
From the information given,
m1 = 1
m2 = 2
r = 2
By substituting these values into the formula,
F = (6.7 x 10^-11 x 1 x 2)/2^2
F = 33.5 x 10^- 12
F = 3.35 x 10^-11
The second option is correct
Imagine that someone is looking out of the top floor window of a skyscraper with a brick in his hand at the same instant someone else is looking out if the window on the floor below also holding a brick if both bricks were dropped at the same instant would the distance between them increase decrease or remain the same over time why
The distance between them remain the same over time both of them are accelerating - because of gravity
What is acceleration ?
acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.
Both of them are accelerating - because of gravity - and the one that you dropped first has been accelerating for longer - and is therefore going faster than they one that you dropped later.
Until the two objects both reach their terminal velocities - assuming the objects are identical - their speeds will eventually be the same - and from that point onwards - the distance between them won’t change
The distance between them remain the same over time both of them are accelerating - because of gravity
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Round the answer for each problem to the correct number of significant figures.
a. (7.31 × 104) + (3.23 × 103)
b. (8.54 × 10–3) – (3.41 × 10–4)
c. 4.35 dm × 2.34 dm × 7.35 dm
d. 4.78 cm + 3.218 cm + 5.82 cm
e. 38,736 km ÷ 4784 km
After solving each problem to correct the number of significant figures :
(a) 76330
(b) 8199 × 10⁻³
(c) 74.81 dm.
(d) 13.8 cm
(e) 8.09 km
What is an Equation?Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left hand side = right hand side) is a fundamental mathematical formula.
According to the question,
(a) (7.31 × 10⁴) + (3.23 × 10³)
(73100) + (3230) = 76330
(b) (8.54 × 10⁻³) – (3.41 × 10⁻⁴)
= 8199 × 10⁻³
(c) 4.35 dm × 2.34 dm × 7.35 dm
= 74.81 dm.
(d) 4.78 cm+3.218 cm+5.82 cm
= 13.8 cm
(e) 38,736 km ÷ 4784 km
= 8.09 km
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Shown in the figure, are electric field lines around two point charges. The two charges might be which of these? A)two protons B)a proton and an electron C)two electrons D)two croutons E)two neutrons
Given:
A figure of the electric field lines.
To find:
The nature of the charges.
Explanation;
The electric field lines always start at a positive charge. And the electric field lines always end at a negative charge. If there is a single charge, the field lines may start at infinity or end at infinity.
Electric field lines also do not form closed loops. They do not cross each other.
In the figure, the field lines start at the blue charge and end at the charge represented by the color yellow.
Therefore the blue charge is positive and the yellow charge is negative.
Final answer:
Therefore the correct answer is option B.
Choose all the answers that apply.Asteroids:only orbit planetsonly orbit the sunare made of frozen gas and icetake millions of years to orbit the sun sometimes come very close to Earth
ANSWER:
5th option: sometimes come very close to Earth
STEP-BY-STEP EXPLANATION:
Asteroids are small rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller.
Therefore, of the options the only totally true option is "sometimes come very close to Earth"
So the correct answer is 5th option: sometimes come very close to Earth
Can you tell me the types of thermal processes and there meanings
Isothermal process: Temperature remains constant
Adiabatic process: No heat is exchanged to or from the system.
Isochoric process : Change in volume is zero.
ISobaric process : Pressure remains constant .
A 60.0 kg skier with an initial speed of 14 m/s coasts up a 2.50 m high rise
Find her final speed right at the top, in meters per second, given that the coefficient of friction between her skis and the snow is 0.38?
The final speed (in meters per second), given that the coefficient of friction between her skis and the snow is 0.38 is 14.65 m/s
How do I determine the final velocity?First, we shall obtain the force. This can be obatined as follow:
Mass (m) = 60 KgAcceleration due to gravity (g) = 9.8 m/s²Normal reaction (N) = mg = 60 × 9.8 = 588 NCoefficient of kinetic friction (μK) = 0.38Force (F) = ?F = μKN
F = 0.38 × 588
F = 223.44 N
Next, we shall obtain the acceleration of the skier. This can be obtained as follow:
Mass (m) = 60Force (F) = 223.44 NAcceleration (a) = ?a = F / m
a = 223.44 / 61
a = 3.724 m/s²
Finally, we shall determine the final velocity. This can be obtained as follow:
Initial speed (u) = 14 m/sDistance (s) = 2.5 mDeceleration (a) = 3.724 m/s²Final speed (v) =?v² = u² + 2as
v² = 14² + (2 × 3.724 × 50)
v² = 196 + 18.62
v² = 214.62
Take the square root of both sides
v = √214.62
v = 14.65 m/s
Thus, the the final speed is 14.65 m/s
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The final speed right at the top will be 14.65 m/s and the coefficient of friction between her skis and the snow is 0.38.
What is velocity?The ratio between displacement to time is referred to as the velocity of the object. It is a vector quantity with SI unit meter per second (m/s).
According to the question, the given information is :
Skier's mass, m = 60 kg
The acceleration due to gravity, g = 9.8 m/s²
Initial Speed, u = 14 m/s
Distance, s = 2.5 m
Deceleration is given as, a = 3.724 m/s².
Normal reaction force (N) will be equal to mg.
N = 60 × 9.8
N = 588 N
The coefficient of kinetic friction is given as, μ = 0.38
By using the formula,
F = μKN
F = 0.38 × 588
F = 223.44 N
Now, let's calculate the acceleration of the skier :
f = ma
a = f/m
a = 223.44/60
a = 3.724 m/s².
Now, calculate the velocity,
v² = u² + 2as
v² = 14² + 2 (3.724) (50)
v² = 196 + 18.62
v² = 214.62
v = 14.65 m/s.
Hence, the final speed right at the top will be 14.65 m/s.
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In which direction does the tension force on the pirate point when a gust of wind rises up?
Answer: For downwind sailing, with the sail oriented perpendicular to the wind direction, the pressure increase on the upwind side is greater than the pressure decrease.
Explanation: this is all i know
Examine the heating curve for water below. Answer each question andcomplete the table to review your understanding of heating curves
Explanation:
When the temperature is increasing, the kinetic energy change, and when the graph is horizontal (the water is changing phases), the potential energy changes.
So at A, C, and E, there is a change in kinetic energy and at B and D there is a change in potential energy.
Then, we use a specific heat capacity of 4.2 J/g°C when the water is at A, C, and E. We use latent heat of 334 J/g for melting and latent heat of 2260 J/g for evaporation.
Answer:
Therefore, the complete table is
When a stone and a feather is thrown down from a height under free fall. Which of the two will first reach the ground???
Answer:
The stone
Explanation:
It will be the first to fall because of its mass which is heavier than that of the feather .
What conditions must be met in order for work to be done?
A. The applied force must make the object move.
B. The output force must be greater than the input force.
C. At least part of the applied force must be in the same direction as the movement of the object.
D. The work must be greater than the momentum.
At least part of the applied force must be in the same direction as the movement of the object must be met in order for work to be done.
What are the conditions to work?The following are the two prerequisites for working: To do the work, the body must be subjected to a force, or F 0. The body must move in the direction of the applied force, or S 0, as a result of the applied force.There must be a force used. The displacement is the distance over which the force must act. The displacement must be a component of the force.A legal term known as a condition precedent refers to an event that must occur before a certain contract is regarded as being in effect or before either party is obliged to fulfill any obligations.
Therefore, the correct answer is option C. At least part of the applied force must be in the same direction as the movement of the object.
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Which of the following scientists discovered that atoms contain electrons?a. Daltonb. RutherfordC. Thomsond. Bohr
Until 1897, atom was thought as the fundemental particle. But in 1897 J.J Thompson discovered that the atoms contains electrons. He discovered during his experiment with cathod ray tube.
Thus the correct answer is option C.
Two sounds of 610Hz and 620Hz are played together. The frequency you hear will be ___. The beat frequency is ___
Explanation
The beat frequency is equal to the complete value of the alteration in the frequency of the two waves,it can be calculated by using the expression
[tex]f_{beat}=\lvert{{f_1}-f_2}\rvert[/tex]so
Step 1
a)let
[tex]\begin{gathered} f_1=610\text{ Hz} \\ f_2=620\text{ Hz} \end{gathered}[/tex]b) replace and calculate
[tex]\begin{gathered} f_{beat}=\lvert{{f_1}-f_2}\rvert \\ f_{beat}=\lvert610\text{ Hz-620Hz}\rvert \\ f_{beat}=10\text{ Hz} \end{gathered}[/tex]so
the beat frequency is 10 HZ
Step 2
the frequency yuo will detect is the difference of the frequency, so , teh frequency beat, so
the frequency you hear will be 10 Hz
I hope this helps you
A construction worker pushes a wheelbarrow 5.0 m with a horizontal force of 250.0 N. How much work is done by the worker on the wheelbarrow
Given data
*A construction worker pushes a wheelbarrow at a distance is d = 5.0 m
*The given horizontal force is F = 250.0 N
The formula for the work is done by the worker on the wheelbarrow is given as
[tex]W=F\times d[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} W=(250.0)(5.0) \\ =1250\text{ J} \end{gathered}[/tex]Hence, the work done by the worker on the wheelbarrow is W = 1250 J
Every 5 seconds, the crest of a wave in the ocean travels 25 meters. What is the speed of the wave?
Given
Every 5 seconds
One wave travel 25m
Speed of waves
Explanation
[tex]\begin{gathered} v=\frac{25m}{5s} \\ v=5\text{ m/s} \end{gathered}[/tex]
The answer would be 5 m/s
which force is used when a rock fell
When something falls, it falls because of gravity. Because that object feels a force, it accelerates, which means its velocity gets bigger and bigger as it falls. The strength with which the Earth pulls on something in the form of gravity is a type of acceleration. Earth pulls on everything the exact same amount. A rockfall is a type of fast-moving landslide that happens when rock or earth falls, bounces, or rolls from a cliff or down a very steep slope. Rockfalls start from high outcrops of hard, erosion-resistant rock that become unstable for a variety of reasons. When a rock is thrown upward, if we exempt the air drag then the only force that is acting on the rock is the gravitational force, also known as the weight of the rock. The acceleration due to gravity is always acting downward.
Answer: The force is Gravity
Explanation:
Gravity is what makes us stay to the ground and if a rock fell it would go to the ground just like if i where to jump i would land on the floor/ground i wont be floating because of gavity.
Have a good day.
The potential energy of two atoms in a diatomic molecule is approximated by U(r)=a/r12−b/r6, where r is the spacing between atoms and a and b are positive constants.
Find the force F(r) on one atom as a function of r .
Express your answer in terms of the variables a , b , and r .
The force (r) on one atom as a function of r is a/r¹³ - b/r⁷.
What is the electric force between charged molecules?
The electric force between charged molecules is determined by applying Coulomb's law, which states that the electric force between tow charged molecules is directly proportional to the product of their charges and inversely proportional to the square of their distance.
F = kq²/r²
where;
q is the magnitude of the chargesr is the distance between the chargesThe electric potential energy of the atoms is given as;
U = Fr
From the given parameters;
Fr = a/r¹² − b/r⁶
F = 1/r( a/r¹² − b/r⁶)
F = a/r¹³ - b/r⁷
Thus, the force on one atom as a function of r is determined by applying Coulomb's law of electrostatic force. The force is also expressed in terms of the variables a , b , and r .
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What is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? The static and kinetic coefficients of friction are, respectively, 0.65 and 0.45. Assume that the surface of the seat is horizontal.
The shortest distance in which you can stop, after the breaks are applied is 80.38 m.
What is the shortest distance you can stop?The shortest distance in which you can stop is calculated by applying the principle of conservation of energy and work energy principle.
K.E = ¹/₂mv²
where;
K.E is your kinetic energy
m is your mass
v is your speed
The work done by force of friction before you stop is calculated as follows;
W = Ffx
where;
Ff is the frictional forcex is the shortest distance you can stopW = (μmg)x
where;
μ is coefficient of kinetic frictionW = K.E
(μmg)x = ¹/₂mv²
(μg)x = ¹/₂v²
x = (v²) / (2μg)
x = (32²) / (2 x 0.65 x 9.8)
x = 80.38 m
Thus, the shortest distance in which you can stop, after the breaks are applied is determined by applying the principle of conservation of energy.
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The complete question is below:
Your are driving at 32 m/s, what is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? The static and kinetic coefficients of friction are, respectively, 0.65 and 0.45. Assume that the surface of the seat is horizontal.
A projectile is fired at an upward angle of 55.0 ∘ from the top of a 155 m cliff with a speed of 165 m/s .
a)What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)
A projectile is fired at an upward angle and the speed of the object when it strikes the ground below will be 434.5 m/s.
What is Projectile motion?A projectile is an object or particle that is thrown toward the surface of the Earth and moves along a curved route only under the influence of gravity. Galileo demonstrated that this curving path was a parabola, but in the unique situation where it is hurled straight up, it may also be a straight line.
According to the question,
[tex]h=v_0_yt+1/2gt^2[/tex]
-155 m = (165 × sin 55°)t - 0.5(9.8)t²
-155 = 135.16t - 4.9 t²
4.9 t² - 135.16t - 155 = 0
t = 27.5 seconds.
Now, the speed of the object when it strikes the ground will be,
[tex]v_f=v_i+gt[/tex]
= 165 + (9.8)(27.5)
[tex]v_f[/tex] = 434.5 m/s.
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Multiple Choice: A car with a mass of 825 kg moves along the roadway at aspeed of 15 m/s to the east. What impulse is required to decrease the speed of theboat to 10 m/s east?
Given:
The mass of the car is m = 825 kg
The intial speed of the car is
[tex]v_i\text{ = 15 m/s}[/tex]towards east.
The final speed of the car is
[tex]v_f\text{ = 10 m/s}[/tex]To find the impulse of the car.
Explanation:
The impulse can be calculated by the formula
[tex]Impulse\text{ = mv}_f-mv_i[/tex]On substituting the values, the impulse will be
[tex]\begin{gathered} Impulse\text{ = \lparen825}\times10\text{\rparen-\lparen825}\times15\text{\rparen} \\ =\text{ -4125 kg m/s} \end{gathered}[/tex]The impulse will be 4125 kg m/s due
Three non-parallel forces which can be represented both in magnitude and direction by the three sides of a triangle, taken in order, can: A. make a body oscillate B. make a body rotate C. keep a body in equilibrium D. move a body in a straight line E. always produce vertical motion of body
Answer:
If the triangle representing the 3 non-colinear forces is closed
then then (C) the body is in equilibrium:
Adding vectors A + B + C = 0 means that the resultant of adding the three vectors A, B, and C is zero
A bungee jumper jumps off a bridge and bounces up and down several times.She finally comes to rest 30 m below the bridge from which she just jumped.If her mass is 50 kg and the spring constant of the bungee cord is 10 N/m,how much energy was lost due to air resistance while she was bouncing?(Recall that g = 9.8 m/s2)A. 9200 NB. 7330 Nc. 10,200 ND. 8605 N
Given data
*The given height is h = 30 m
*The given mass is m = 50 kg
*The spring constant of bungee cord is k = 10 N/m
*The value of the acceleration due to the gravity is g = 9.8 m/s^2
The net change in potential energy is calculated as
[tex]\begin{gathered} \Delta U_p=mgh \\ =(50)(9.8)(30) \\ =14700\text{ J} \end{gathered}[/tex]The spring stretch is calculated by using the relation as
[tex]\begin{gathered} F=mg \\ kx=mg \\ x=\frac{mg}{k} \\ =\frac{(50)(9.8)}{10} \\ =49\text{ m} \end{gathered}[/tex]The energy stored in spring is calculated as
[tex]\begin{gathered} U_s=\frac{1}{2}kx^2 \\ =\frac{1}{2}(10)(49)^2 \\ =12005 \end{gathered}[/tex]The energy was lost due to air resistance while she was bouncing is calculated as
[tex]\begin{gathered} \Delta E=\Delta U_p-U_s_{}_{} \\ =14700-12005 \\ =2695\text{ J} \end{gathered}[/tex]Hence, the energy was lost due to air resistance while she was bouncing is 2695 J
how many joules does a lamp marked 12 volts, 24 w consumed in an hour . And also what is the current?
Given data:
* The voltage given is 12 volts.
* The value of the power given is 24 Watt.
* The time till which the lamp is used is,
[tex]\begin{gathered} t=1\text{ hr} \\ t=60\times60\text{ s} \\ t=3600\text{ s} \end{gathered}[/tex]Solution:
(a). The energy consumed by the lamp in time t is,
[tex]E=P\times t[/tex]where P is the power of lamp, t is the time, and E is the energy consumed,
Substituting the known values,
[tex]\begin{gathered} E=24\times3600 \\ E=86400\text{ J} \\ E=86.4\times10^3\text{ J} \\ E=86.4\text{ kJ} \end{gathered}[/tex]Thus, the energy consumed by the lamp in 1 hour is 86.4 kJ.
(b). The power of the lamp in terms of voltage and current is,
[tex]\begin{gathered} P=VI \\ I=\frac{P}{V} \end{gathered}[/tex]where P is the power, V is the voltage and I is the current,
Substituting the known values,
[tex]\begin{gathered} I=\frac{24}{12} \\ I=2\text{ A} \end{gathered}[/tex]Thus, the current flowing through the lamp is 2 A.
1. Consider the example problem, but with the lower pressure reduced to 100 Pa. How much work would be done in a single cycle?1. 29,970 J2. 0 J3. -30,030 J4. 27,000 J
29970 J
Explanation:Given:
[tex]\begin{gathered} P_A=P_B=10^5Pa \\ P_c=P_D=100\text{ Pa\lparen The new lower pressure\rparen} \\ V_A=V_D=0.1m^3 \\ V_B=V_C=0.4m^3 \end{gathered}[/tex]Work done across AB
[tex]\begin{gathered} W_{AB}=P_{AB}(V_B-V_A) \\ \\ W_{AB}=10^5(0.4-0.1) \\ \\ W_{AB}=0.3\times10^5 \\ \\ W_{AB}=30000J \end{gathered}[/tex]Work done across BC = 0 J (Since there is no change in volume)
Work done across DA = 0 J (Since there is no change in volume)
Work done across CD
[tex]\begin{gathered} W_{CD}=P_{CD}(V_D-V_C) \\ \\ W_{CD}=100(0.1-0.4) \\ \\ W_{CD}=100(-0.3) \\ \\ W_{CD}=-30J \end{gathered}[/tex]Work done in one cycle:
[tex]\begin{gathered} W_{cycle}=W_{AB}+W_{BC}+W_{DA}+W_{CD} \\ \\ W_{cycle}=3000J+0+0-30 \\ \\ W_{cycle}=29970J \end{gathered}[/tex]29970J of work will be done in a single cycle
Rtz coordinate system
Due to the car goes around the trajectory without sliding, then. it is necessary that centripetal force equals the friction force.
Then, we have:
Fc = Fr
where,
Fc = m(v^2/R) centripetal force
Fr = μN = μ*m*g friction force
Then, by replacing the precious expressions we obtain:
m(v^2/R) = μ*m*g
And by solving for v:
[tex]v=\sqrt[]{\mu\cdot g\cdot R}[/tex]where,
μ = 1.00
g = 9.8 m/s^2
R = 70.0 m
By replacing we get:
[tex]undefined[/tex]
True/False: The only difference between how electricity is produced at a coal plant and at a nuclear reactor is the type of fuel used to heat the water to steam. Select one:TrueFalse
To determine whether the given statement is true/false.
Explanation:
In nuclear reactors, after nuclear fission, energy is generated in the form of heat. This heat is used convert water steam.
In coal plant, burning coal produces steam.
Thus, the statement is true.