Answer:
False.
Explanation:
From Kepler's Third Law of plenetary motion, we know that:
<em>"The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."</em>
Or, as expressed in mathematical terms:
, where <em>a</em> is the semi-major axis of the orbit (the distance from the center), and <em>T </em>is the orbital period of the satellite.
From this expression we can clearly see that if the orbit's semi-major axis is doubled, orbital period will be 
times longer to compensate the variation.
Answer:
E = 1/2 M V^2 + 1/2 I ω^2 = 1/2 M V^2 + 1/2 I V^2 / R^2
E = 1/2 M V^2 (1 + I / (M R^2))
For a cylinder I = M R^2
For a sphere I = 2/3 M R^2
E(cylinder) = 1 + 1 = 2 omitting the 1/2 M V^2
E(sphere) = 1 + 2/3 = 1.67
E(cylinder) / E(sphere) = 2 / 1.67 = 1.2
The cylinder initially has 1.20 the energy of the sphere
The PE attained is proportional to the initial KE
H(sphere) = 2.87 / 1/2 = 2.40 m since it has less initial KE
Answer: 0.0180701 s
Explanation:
Given the following :
Length of string (L) = 10 m
Weight of string (W) = 0.32 N
Weight attached to lower end = 1kN = 1×10^3
Using the relation:
Time (t) = √ (weight of string * Length) / weight attached to lower end * acceleration due to gravity
g = acceleration due to gravity = 9.8m/s^2
Weight of string = 0.32N
Time(t) = √ (0.32 * 10) / [(1*10^3) * (9.8)]
Time = √3.2 / 9800
= √0.0003265
= 0.0180701s
Answer:
10.4mm
Explanation:
2 pages = 1 leaf
200 pages = 100 leaves
100 × 0.10 = 10 mm thickness
Total thickness = 2(0.20) +10 = 0.4+10 = 10.4mm
Answer:
230 N
Explanation:
At the lowest position , the velocity is maximum hence at this point, maximum support force T is given by the branch.
The swinging motion of the ape on a vertical circular path , will require
a centripetal force in upward direction . This is related to weight as follows
T - mg = m v² / R
R is radius of circular path . m is mass of the ape and velocity is 3.2 m/s
T = mg - mv² / R
T = 8.5 X 9.8 + 8.5 X 3.2² / .60 { R is length of hand of ape. }
T = 83.3 + 145.06
= 228.36
= 230 N ( approximately )
