Answer:
.
Explanation:
When the ball is placed in this pool of water, part of the ball would be beneath the surface of the pool. The volume of the water that this ball displaced is equal to the volume of the ball that is beneath the water surface.
The buoyancy force on this ball would be equal in magnitude to the weight of water that this ball has displaced.
Let
denote the mass of this ball. Let
denote the mass of water that this ball has displaced.
Let
denote the gravitational field strength. The weight of this ball would be
. Likewise, the weight of water displaced would be
.
For this ball to stay afloat, the buoyancy force on this ball should be greater than or equal to the weight of this ball. In other words:
.
At the same time, buoyancy is equal in magnitude the the weight of water displaced. Thus:
.
Therefore:
.
.
In other words, the mass of water that this ball displaced should be greater than or equal to the mass of of the ball. Let
denote the density of water. The volume of water that this ball should displace would be:
.
Given that
while
:
.
In other words, for this ball to stay afloat, at least
of the volume of this ball should be under water. Therefore, the volume of this ball should be at least
.
Answer:
The capacitance of your capacitor is 5.476 x 10⁻⁵ μF
Explanation:
Given;
diameter of the aluminum pie plates = 16 cm = 0.16 m
separation distance, d = 3.25 mm = 0.00325 m
voltage across the parallel plates = 6 V

where;
C is the capacitance of your capacitor
ε is the permittivity of free space = 8.85 x 10⁻¹² (F/m)
d is separation distance
A is the area of the plate = ¹/₄ (πd²) = 0.25 (π x 0.16²) = 0.02011 m²

Therefore, the capacitance of your capacitor is 5.476 x 10⁻⁵ μF
Answer:
speed of water is 0.0007138m/s
Explanation:
From the law of conservation of mass
Rate of mass accumulation inside vessel = mass flow in - mass flow out
so, dm/dt = mass flow in - mass flow out
taking p as density

where,
q(in) is the volume flow rate coming in
Q = is the volume of liquid inside tank at any time
But,
dQ = Adh
where ,
A = area of liquid surface at time t
h = height from bottom at time t
A = πr²
r is the radius of liquid surface

Hence,


so, the speed of water surface at height h

where,
is 75.7 L/min = 0.0757m³/min
h = 1.5m
so,

v = 0.04283 /60
v = 0.0007138m/s
Hence, speed of water is 0.0007138m/s