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A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the...


A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15 degrees and rolls to the bottom. The upper end of the ramp is 2.0 m higher than the lower end. What is the linear velocity when it reaches the bottom of the ramp?

A. 4.7 m/s
B. 4.1 m/s
C. 3.4 m/s
D. 5.3 m/s
E. 1.8 m/s
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Answer #1

When sphere is placed on the top of the inclined plane then it has only potential enegy.as it rolls down then its potential energy is converted into linear kinetic energy and rotational kinetic energy.when it reaches to the bottom then its whole potential energy is converted into partly into translational kinetic energy and partly into rotational kinetic energy.

from Law of conservation of energy-

Potential energy at the top=(Translation+rotational) K.E. at the bottom

     ---------------------------------(1)

But for solid sphere moment of inertia-

  

and

using above in equation(1)

Hence option D is correct...

(If further have any doubt then comment me...)

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