Answer:
Car C
Explanation:
The length of the deformed crumple zone is significantly longer in Car C, so the average deceleration was lower. The lower acceleration puts less stress on the dummy. Car C better protected the dummy.
Answer
a) Using dimensional analysis we cannot derive the relation, But we can check the correctness of the formula.
![s = u t +\dfrac{1}{2}at^2](https://tex.z-dn.net/?f=s%20%3D%20u%20t%20%2B%5Cdfrac%7B1%7D%7B2%7Dat%5E2)
now, L H S
s = distance
dimension of distance = [M⁰L¹T⁰]
now, equation on the right hand side
R H S
u = speed
u = m/s
Dimension of speed = [M⁰L¹T⁻¹]
dimension of time
t = sec
Dimension of time = [M⁰L⁰T¹]
Dimension of 'ut' = [M⁰L¹T⁻¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
now, acceleration= a
a = m /s²
dimension of acceleration = [M⁰L¹T⁻²]
dimension of (at²) = [M⁰L¹T⁻²][M⁰L⁰T¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
hence, the dimension are balanced.
so, L H S = R H S
b) Moment of inertia of hollow sphere = ![\dfrac{2}{3}Mr^2](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B3%7DMr%5E2)
Moment of inertia of solid sphere = ![\dfrac{2}{5}Mr^2](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B5%7DMr%5E2)
we know,
![\tau = I \alpha](https://tex.z-dn.net/?f=%5Ctau%20%3D%20I%20%5Calpha)
![\alpha=\dfrac{\tau}{I}](https://tex.z-dn.net/?f=%5Calpha%3D%5Cdfrac%7B%5Ctau%7D%7BI%7D)
Torque is the force that causes rotation
If the same amount of torque is applied to both spheres the sphere with bigger moment of inertia would have smaller angular velocity.
Thus the solid sphere would accelerate more.
Ha! Lot of words but the question itself is easy.
The answer is 2.5 times 10 to the 5th power.
The main part of the numbers has the decimal point placed after the first digit.
Then for what number of power, you just count the number of decimal places moved.
I hope this helps you.
A hypothesis is an educated guess. It refers to a theory you have based on some sort of evidence you collected or noticed. It is not fact and can sometimes be proven wrong. A law would refer to a scientific fact that has been proven correct and is a fact about the subject.