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Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.
A body rolling on an inclined plane of height h,is shown in the following figure:
m = Mass of the body
R = Radius of the body
K = Radius of gyration of the body
v = Translational velocity of the body
h =Height of the inclined plane
g = Acceleration due to gravity
Total energy at the top of the plane, E1= mgh
Total energy at the bottom of the plane,
But
From the law of conservation of energy, we have:
Hence, the given result is proved.
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