The area of the top and bottom:
2πr²
Cost for top and bottom:
2πr² x 0.02
= 0.04πr²
Area for side:
2πrh
Cost for side:
2πrh x 0.01
= 0.02πrh
Total cost:
C = 0.04πr² + 0.02πrh
We know that the volume of the can is:
V = πr²h
h = 500/πr²
Substituting this into the cost equation to get a cost function of radius:
C(r) = 0.04πr² + 0.02πr(500/πr²)
C(r) = 0.04πr² + 10/r
Now, we differentiate with respect to r and equate to 0 to obtain the minimum value:
0 = 0.08πr - 10/r²
10/r² = 0.08πr
r³ = 125/π
r = 3.41 cm
Answer: The final volume V₂ of the container is 0.039 m³.
Explanation:
Since the temperature is constant, the gas would expand isothermally.
For isothermal expansion,
P₁V₁=P₂V₂
Where, P₁ and P₂ are the initial and final pressure and V₁ and V₂ are initial and final volume.
It is given that:
V₁ = 0.0250 m³
P₁ = 1.5 × 10⁶ Pa
P₂ = 0.950 × 10⁶ Pa
V₂ = ?
⇒ 1.5 × 10⁶ Pa × 0.0250 m³ = 0.950 × 10⁶ Pa × V₂
⇒V₂ = 0.039 m³
Hence, the final volume V₂ of the container is 0.039 m³.
Density is mass divides by volume, so
89.6g / 10cm^3 =8.96g /cm^3
*cm^3 is a standard unit of volume*
Answer:
Explanation:
Given:
The accelerated energy, U = 1.25 MeV = 1.25 × 10⁶ eV
we know,
1 eV = 1.6 × 10⁻¹⁹ J
thus,
1.25 eV = (1.6 × 10⁻¹⁹) × (1.25) J = 2 × 10⁻¹³ J
Now, Applying the law of conservation of energy, the energy due to acceleration will be equal to the kinetic energy
mathematically,
K.E = U
where,
m = mass of the particle = 1.67 × 10⁻²⁷ kg
v = velocity of the particle
on substituting the values we get
or
or
or
