Qstnid -11- Torques Of Equal Magnitude Are Applied To A Hollow Cylinder And A Solid Sphere, Both Having The Same Mass And Radius. The Cylinder Is Free To Rotate About Its Standard Axis Of Symmetry, And The Sphere Is Free To Rotate About An Axis Passing Through Its Centre. Which Of The Two Will Acquire A Greater Angular Speed After A Given Time? - 07: System Of Particles And Rotational Motion - Neet-xi-physics

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NEET-XI-Physics

07: System of particles and Rotational Motion

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#11
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
Ans : Let M be the mass and R the radius of the hollow cylinder, and also of the solid sphere. Their moments of inertia about the respective axes are I₁ = MR² and I₂ = 2/5 MR²

Let τbe the magnitude of the torque applied to the cylinder and the sphere, producing angular accelerations α₁andα₂ respectively. Thenτ=I₁ α₁= I₂ α₂

The angular acceleration 04 produced in the sphere is larger. Hence, the sphere will acquire larger angular speed after a given time.