Answer:
The height is 
A circular hoop of different diameter cannot be released from a height 30cm and match the sphere speed because from the conservation relation the speed of the hoop is independent of the radius (Hence also the diameter )
Explanation:
From the question we are told that
The height is 
The angle of the slope is 
According to the law of conservation of energy
The potential energy of the sphere at the top of the slope = Rotational kinetic energy + the linear kinetic energy
Where I is the moment of inertia which is mathematically represented as this for a sphere
The angular velocity 
is mathematically represented as
So the equation for conservation of energy becomes
![mgh_s = \frac{1}{2} [\frac{2}{5} mr^2 ][\frac{v}{r} ]^2 + \frac{1}{2}mv^2](https://tex.z-dn.net/?f=mgh_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5B%5Cfrac%7B2%7D%7B5%7D%20mr%5E2%20%5D%5B%5Cfrac%7Bv%7D%7Br%7D%20%5D%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
![mgh_s = \frac{1}{2} mv^2 [\frac{2}{5} +1 ]](https://tex.z-dn.net/?f=mgh_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%20%5B%5Cfrac%7B2%7D%7B5%7D%20%2B1%20%5D)
![mgh_s = \frac{1}{2} mv^2 [\frac{7}{5} ]](https://tex.z-dn.net/?f=mgh_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%20%5B%5Cfrac%7B7%7D%7B5%7D%20%5D)
![gh_s =[\frac{7}{10} ] v^2](https://tex.z-dn.net/?f=gh_s%20%3D%5B%5Cfrac%7B7%7D%7B10%7D%20%5D%20v%5E2)
Considering a circular hoop
The moment of inertial is different for circle and it is mathematically represented as
Substituting this into the conservation equation above
![mgh_c = \frac{1}{2} (mr^2)[\frac{v}{r} ] ^2 + \frac{1}{2} mv^2](https://tex.z-dn.net/?f=mgh_c%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28mr%5E2%29%5B%5Cfrac%7Bv%7D%7Br%7D%20%5D%20%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
Where 
is the height where the circular hoop would be released to equal the speed of the sphere at the bottom
Recall that
Substituting values
When a force applied to a breaker bar the torque can be calculated by multiplying the<u> length of the lever</u> by the tangential component of force on the lever.
<h3>What is torque?</h3>
Torque is the <u>rotating equivalent</u> of force in physics and mechanics. Depending on the subject of study, it is also known as the moment, moment of force, rotating force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion.
Torque is given by the formula :
α = r x F ( bold letters represent vector quantities)
The S.I. unit for torque is : N - m ( Newton - meter)
<h3>How do we define 1 N-m of torque?</h3>
The newton-metre is a torque unit (also known as a moment) in the SI system. The torque produced by a one newton force applied <u>perpendicularly to the end of a one metre long</u> moment arm is known as a newton-metre.
To learn more about torque:
brainly.com/question/14970645
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Answer:
net force is positive downward..B
The correct answer is A because the main disorder is schizophrenia. It includes all the previous subtypes: catatonic, disorganized, paranoid, residual, and undifferentiated. It's a psychosis, which means that what seems real to you isn't.
When the initial speed given is 7.5m/s at an angle of 27° , ball will go
4.637 meters.
Assume no air opposition to the ball ;
Vertical component of ball is sin 27° = 0.453
0.453* 7.5 = 3.404 meters /sec
Time taken to reach ground is :
3.404 = -3.404+9.8*t
t= 6.808/9.8= 0.694 sec
Horizontal component is 7.5*cos27°= 6.682m/s
Distance = speed * time
=6.682 * 0.694
=4.637 meters
Horizontal distance it can cover in 0.694 sec is 4.637 meters
So range of ball is 4.637 meters.
Form of motion experienced by an object or particle that is projected near surface of the earth and moves along a curve is called Projectile motion. Three types of projectile motion are Horizontal projectile motion. Oblique projectile motion and Projectile motion on an inclined plane.
To know more about projectile motion, refer
brainly.com/question/24216590
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