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Q.

Consider three solid spheres, sphere (i) has radius r and mass m, sphere (ii) has radius r and mass 3m,
sphere (iii) has radius 3r and mass m. All can be placed at the same point on the same inclined plane, where they will roll without slipping to the bottom. If allowed to roll down the incline, then at the bottom of the incline, choose the correct statement. 

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a

Sphere (i) will have the largest speed.

b

Sphere (ii) will have the largest speed.

c

Sphere (iii) will have the largest kinetic energy.

d

All the spheres will have equal speeds.

answer is D.

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Detailed Solution

Acceleration, a=gsinθ1+Imr2

For a sphere,  Imr2=25

Hence,  a=57gsinθ= constant. 

Hence, speeds of all spheres will be same at the bottom. Sphere (ii) has the largest mass. 

Hence, it will have the maximum kinetic energy.

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