Answer:
Explanation:
The pressure of the gas can be found out as follows
Gas law formula is as follows
PV = nRT
P = nRT / V
= 32.4 X 8.31 X ( 273 + 459.38 ) / 51 X 10⁻⁶
3866.45 X 10⁶ Pa.
The first change is isobaric therefore
V₁ / T₁ = V₂ / T₂
V₂ = V₁ X T₂/ T₁
= 51 X 10⁻⁶ X ( 855.6 +273) / (459.38 +273)
= 78 X 10⁻⁶
78 cm³
After the first operation , the pressure of the gas remains at
= 3866.45 X 10⁶ Pa.
Now volume of the gas changes from 78 cm³ to 25.3 cm³ isothermally so
P₁V₁ = P₂V₂
P₂ = P₁V₁ / V₂
= 3866.45 X 10⁶ X 78 / 25.3
= 11920 X 10⁶ . Pa
Answer:
the dimensions of the rectangle are:
l = 50 m
b =
Solution:
As per the question:
Perimeter of the room, P = 200 m
The region is rectangular having a semicircle at each end.
Now,
Let 'l' be the length of the rectangle, 'b' be its breadth and 'r' be the radius of the semi-circle at each end.
Then
Area of the rectangle, A = lb
Perimeter of the room, P =
Therefore, we can write:
Now,
Area, A =
Now, differentiate A w.r.t l:
Again differentiating w.r.t 'l', we get:
< 0
Thus we get maximum are when
Therefore,
l = 50 m
Now, from
b =
r =
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Answer:
770.1 m
Explanation:
From the question given above, the following data were obtained:
Velocity (v) = 45.3 m/s
Time (t) = 17 s
Displacement (d) =?
Velocity is defined according to the following formula:
Velocity = Displacement /Time
With the above formula, we can obtain the displacement of the ball as follow:
Velocity = Displacement /Time
45.3 = Displacement / 17
Cross multiply
Displacement = 45.3 × 17
Displacement = 770.1 m
Therefore the displacement of the ball is 770.1 m
Answer:
1.06 secs
Explanation:
Initial speed of sled, u = 8.4 m/s
Final speed of sled, v = 5.8 m/s
Coefficient of kinetic friction, μ = 0.25
Using the impulse momentum theory, we know that the impulse applied to the sled is equal to change in momentum of the sled:
FΔt = mv - mu
where m = mass of the object
Δt = time interval
F = force applied
The force applied on the sled is the frictional force, which is given as:
F = -μmg
where g = acceleration due to gravity
Therefore:
-μmgΔt = mv - mu
-μmgΔt = m(v - u)
-μgΔt = v - u
Making Δt subject of formula:
Δt = (v - u) / -μg
Δt = (5.8 - 8.4) / (-0.25 * 9.8)
Δt = -2.6/ -2.45
Δt = 1.06 secs
It took the sled 1.06 secs to travel from A to B.