The helium may be treated as an ideal gas, so that
(p*V)/T =constant
where
p = pressure
V = volume
T = temperature.
Note that
7.5006 x 10⁻³ mm Hg = 1 Pa
1 L = 10⁻³ m³
Given:
At ground level,
p₁ = 752 mm Hg
= (752 mm Hg)/(7.5006 x 10⁻³ mm Hg/Pa)
= 1.0026 x 10⁵ Pa
V₁ = 9.47 x 10⁴ L = (9.47 x 10⁴ L)*(10⁻³ m³/L)
= 94.7 m³
T₁ = 27.8 °C = 27.8 + 273 K
= 300.8 K
At 36 km height,
P₂ = 73 mm Hg = 73/7.5006 x 10⁻³ Pa
= 9.7326 x 10³ Pa
T₂ = 235 K
If the volume at 36 km height is V₂, then
V₂ = (T₂/p₂)*(p₁/T₁)*V₁
= (235/9.7326 x 10³)*(1.0026 x 10⁵/300.8)*94.7
= 762.15 m³
Answer: 762.2 m³
Answer:
b) R/4 (There seems to an error in mentioning the multiple choices of this question, please see below explanation of correct calculations for this question.)
Explanation:
dimension of the conductor before melting is l, r
reistivity is p
R=(p*l)/(pie*r2)
after reforming length is reduced to L=l/4
volume in both the cases will be same
i.e. pie * r^2 * l =pie * R^2 * L
r^2 * l = R^2 * (1/2)l
due to this radius will become R=sqrt(2) * r
now new reistance is given by Rx=(p * L)/(pie * R^2)
i.e. Rx=(p * l/2)/(pie * r^2 * 2)
after simplification RX=((p * l)/(pie * r^2))/4
i.e. Rx=R/4
The tennis ball lands at a point 40.4 m from the base of the building.
The tennis ball is projected with a horizontal velocity <em>u</em> from a window, which is at a height <em>y</em> from the ground. The ball lands at a distance <em>x</em> from the base of the building. Let the ball take a time <em>t</em> to reach the ground. In the time <em>t</em> ,the ball falls a vertical distance <em>y</em> and also travel a horizontal distance <em>x</em>.
The initial vertical velocity of the ball is zero, since the ball is projected in the horizontal direction. The ball falls down under the action of gravitational force.
Thus, use the equation of motion,

rewrite the expression for <em>t</em> and calculate the value of <em>t</em> using 9.81 m/s²for <em>g</em> and 500 m for <em>y</em>.

The horizontal distance <em>x</em> is traveled using the constant velocity <em>u </em>since no force acts on the ball in the horizontal direction.
Therefore,

Substitute 4 m/s for <em>u</em> and 10.096 s for <em>t</em>

Thus, the ball lands at a point 40.4 m from the base of the building.