A solid cylinder and a hollow cylinder of the same mass and radius are released
Practice Questions
Q1
A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one reaches the ground first? (2022)
Solid cylinder
Hollow cylinder
Both reach at the same time
Depends on the height
Questions & Step-by-Step Solutions
A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one reaches the ground first? (2022)
Step 1: Understand that both cylinders are released from the same height and have the same mass and radius.
Step 2: Know that when objects roll down a slope, their shape affects how they move. This is described by something called 'moment of inertia.'
Step 3: Recognize that a solid cylinder has a lower moment of inertia compared to a hollow cylinder. This means it is easier for the solid cylinder to start rolling.
Step 4: Since the solid cylinder accelerates faster due to its lower moment of inertia, it will reach the ground before the hollow cylinder.
Step 5: Conclude that the solid cylinder reaches the ground first.
Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. A lower moment of inertia means the object can accelerate more quickly when rolling.
Rolling Motion – When objects roll down an incline, both translational and rotational motions are involved, affecting their acceleration and final velocity.
Energy Conservation – The total mechanical energy (potential + kinetic) is conserved in the absence of non-conservative forces, which influences how quickly each cylinder reaches the ground.
