Answer:
e. 27 rho.
Explanation:
The density of an object, assumed constant, is defined as the relationship between the mass and the volume.
If the object is compressed in such a way that the diameter is reduced to 1/3, this means, that the radius will be reduced in the same proportion.
Now, if the mass remains the same (the compression can't change it) , the volume (assumed to be a perfect sphere) will be reduced also:
V₀ = 4/3*π*r³
Vf= 4/3*π*(r/3)³ = 4/3*π*(r³/27) = V₀/27
As the volume is in in the denominator of the expression for density, this means that the new density will be equal to 27 times the original one:
ρ₀ = m/ V₀
ρ₁ = m/ V₁ = m/ (V₀/27) = 27* (m/V₀) = 27*ρ₀
Answer:
(1) 
(2) Diagram has been attached in the solution.
Explanation:
This question is from projectile motion.
From the given question, we will discuss the motion of the basket ball only in the vertical direction from which we will be able to find out the angle of the initial velocity with the horizontal with which it should be shoot to enter the hoop.
Part (1):
Let us assume:
= initial position of the basket ball = 2.1 m
= final position of the basket ball = 3.05 m
= acceleration of the ball along the vertical = 
= time taken to reach the goal = 0.8 s
= angle of the initial velocity with the horizontal
= initial speed of the ball = 7 m/s
= initial vertical velocity of the ball = u\sin \theta
Using the equation of motion for constant acceleration, we have

Hence, the angle of the shoot of the basket ball with the horizontal is
such that it reaches the hoop on time.
Part (2):
For this part, a diagram has been attached.
Answer:
the <em>ratio F1/F2 = 1/2</em>
the <em>ratio a1/a2 = 1</em>
Explanation:
The force that both satellites experience is:
F1 = G M_e m1 / r² and
F2 = G M_e m2 / r²
where
- m1 is the mass of satellite 1
- m2 is the mass of satellite 2
- r is the orbital radius
- M_e is the mass of Earth
Therefore,
F1/F2 = [G M_e m1 / r²] / [G M_e m2 / r²]
F1/F2 = [G M_e m1 / r²] × [r² / G M_e m2]
F1/F2 = m1/m2
F1/F2 = 1000/2000
<em>F1/F2 = 1/2</em>
The other force that the two satellites experience is the centripetal force. Therefore,
F1c = m1 v² / r and
F2c = m2 v² / r
where
- m1 is the mass of satellite 1
- m2 is the mass of satellite 2
- v is the orbital velocity
- r is the orbital velocity
Thus,
a1 = v² / r ⇒ v² = r a1 and
a2 = v² / r ⇒ v² = r a2
Therefore,
F1c = m1 a1 r / r = m1 a1
F2c = m2 a2 r / r = m2 a2
In order for the satellites to stay in orbit, the gravitational force must equal the centripetal force. Thus,
F1 = F1c
G M_e m1 / r² = m1 a1
a1 = G M_e / r²
also
a2 = G M_e / r²
Thus,
a1/a2 = [G M_e / r²] / [G M_e / r²]
<em>a1/a2 = 1</em>
Answer:
19.33°C
Explanation:
To find the value of T you use the following formula:

v: speed of sound
To calculate v you use:

λ: wavelength = 0.651m
f: = 545Hz
by replacing :

Finally, by replacing in the first formula you obtain:

T = 19.33°C
Answer:
electricity
If a rod is charged it is because of the electrical force acting on it