<h2>
Option 2 is the correct answer.</h2>
Explanation:
Elastic collision means kinetic energy and momentum are conserved.
Let the mass of object be m and M.
Initial velocity object 1 be u₁, object 2 be u₂
Final velocity object 1 be v₁, object 2 be v₂
Initial momentum = m x u₁ + M x u₂ = 3 x 8 + M x 0 = 24 kgm/s
Final momentum = m x v₁ + M x v₂ = 3 x v₁ + M x 6 = 3v₁ + 6M
Initial kinetic energy = 0.5 m x u₁² + 0.5 M x u₂² = 0.5 x 3 x 8² + 0.5 x M x 0² = 96 J
Final kinetic energy = 0.5 m x v₁² + 0.5 M x v₂² = 0.5 x 3 x v₁² + 0.5 x M x 6² = 1.5 v₁² + 18 M
We have
Initial momentum = Final momentum
24 = 3v₁ + 6M
v₁ + 2M = 8
v₁ = 8 - 2M
Initial kinetic energy = Final kinetic energy
96 = 1.5 v₁² + 18 M
v₁² + 12 M = 64
Substituting v₁ = 8 - 2M
(8 - 2M)² + 12 M = 64
64 - 32M + 4M² + 12 M = 64
4M² = 20 M
M = 5 kg
Option 2 is the correct answer.
1. Ideal Mechanical Advantage (IMA): 9
Explanation:
For a wheel and axle system like the steering wheel, the IMA is given by:

where
is the radius of the wheel
is the radius of the axle
For the steering wheel of the problem, we see that
and
, so the IMA is

2. Efficiency: 88.9%
Explanation:
The efficiency of a system is defined as the ratio between the AMA (actual mechanical advantage) and the IMA:

In this problem, AMA=8 and IMA=9, so the efficiency is

Answer:
angular speed of both the children will be same
Explanation:
Rate of revolution of the merry go round is given as
f = 4.04 rev/min
so here we have

here we know that angular frequency is given as



now this is the angular speed of the disc and this speed will remain same for all points lying on the disc
Angular speed do not depends on the distance from the center but it will be same for all positions of the disc
To solve this problem it is necessary to apply the concepts related to frequency as a function of speed and wavelength as well as the kinematic equations of simple harmonic motion
From the definition we know that the frequency can be expressed as

Where,


Therefore the frequency would be given as


The frequency is directly proportional to the angular velocity therefore



Now the maximum speed from the simple harmonic movement is given by

Where
A = Amplitude
Then replacing,


Therefore the maximum speed of a point on the string is 3.59m/s
Wave speed = frequency * wavelength
Wave speed = 4 * 25
Wave speed = 100 m/s