If a hoop and a cylinder of the same mass and radius are realeased from rest...

If a hoop and a cylinder of the same mass and radius are realeased from rest at the top of an incline at the same time, which one will reach the bottom first?

Solutions

Expert Solution

The cylinder will reach the bottom first.

The rolling of object without slipping acceleration depends upon gravity , angle of inclination and moment of inertia of the object.and since acceleration due to gravity and angle of inclined plane is same for both the object so, only thing the motion of the object depends upon is the moment of inertia.

and we know that moment of inertia is nothing but the resistance offered to the rotational motion of the object.

so finally the object with the least moment of inertia between the two,( cylinder and loop) would reach the bottom of the inclined plane first than the other with greater moment of inertia. also the mass and radius are same for both the object then we need to consider overall value of moment of inertia itself.

moreover,

moment of inertia of a cylinder = 1/2 MR²

moment of inertia of a hoop = MR²

so, cylinder has a least value M.I so it will reach the bottom of the inclined plane first.

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A coin and a ring have the same mass and radius. Starting from rest and the...

A coin and a ring have the same mass and radius. Starting from rest and the same height, they roll down the same incline. In other words, they both start with the same gravitational potential energy. Which one of the following statements is true about the coin and ring when they reach the bottom of the incline? A. The increase in the coin's total kinetic energy is less than the increase in the ring's total kinetic energy. B. The increase...

A hoop with a mass of 3.15 kg starts from rest at the top of a...

A hoop with a mass of 3.15 kg starts from rest at the top of a ramp. The ramp is 5.0 m long and 2.1 m high. What is the rotational kinetic energy of the hoop after it has rolled without slipping to the bottom? 16 J 32 J 22 J 78 J

Three different-shapes rolling objects of the same radius and mass are released from rest at the...

Three different-shapes rolling objects of the same radius and mass are released from rest at the same elevation at the same time and roll without slipping) down an inclined plane, the one which finishes first is the one with Select one: a. The smallest moment of inertia b. The second- smallest moment of inertia c. They all finish at the same time d. The second- largest moment of inertia e. The largest moment of inertia

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius....

A solid homogeneous cylinder and a solid homogeneous sphere each have the same mass and radius. They both roll without slipping, have the same linear speed and approach the same inclined plane. As they roll up the inclined plane, they continue to roll without slipping. Which object will reach the greatest height on the inclined plane? A: solid homogeneous cylinder B: solid homogeneous sphere C: they both reach the same maximum height If you could explain why in your answer...

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial kinetic energy.

A hoop, a solid disk, and a solid sphere, all with the same mass and the same radius, are set rolling without slipping up an incline, all with the same initial kinetic energy. Which goes furthest up the incline? The hoop The disk The sphere They all roll to the same height Briefly explain your answer to the previous question. The same three objects as in the previous question are set rolling without slipping up an incline, all with the same initial linear speed. Which goes farthest...

Two smooth spheres of radius are placed inside a cylinder of radius R. The mass of...

Two smooth spheres of radius are placed inside a cylinder of radius R. The mass of each sphere is M Assume that R < 2r < 2R All answers should be in terms of . R.M and What is the force of the bottom sphere on the top sphere? What is the force of the cylinder wall on the top sphere ?

In the figure, a solid cylinder of radius 16 cm and mass 7.7 kg starts from...

In the figure, a solid cylinder of radius 16 cm and mass 7.7 kg starts from rest and rolls without slipping a distance L = 4.4 m down a roof that is inclined at angle θ = 32°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 5.3 m. How far horizontally from the roof's edge does the cylinder hit the level ground?

An green hoop with mass mh = 2.5 kg and radius Rh = 0.12 m hangs...

An green hoop with mass mh = 2.5 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.2 kg and radius Rd = 0.09 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 4.3 kg and radius Rs = 0.22 m....

An green hoop with mass mh = 2.7 kg and radius Rh = 0.16 m hangs...

An green hoop with mass mh = 2.7 kg and radius Rh = 0.16 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.3 kg and radius Rd = 0.1 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 4.2 kg and radius Rs = 0.24 m....

An green hoop with mass mh = 2.7 kg and radius Rh = 0.16 m hangs...

Subjects