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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

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all the spheres will have equal speeds

sphere (i) will have the largest speed

sphere (ii) will have the largest speed

sphere (ii) will have the largest kinetic energy of translation .

answer is C, D.

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Detailed Solution

$a = \frac{g \sin θ}{1 + \frac{I}{m r^{2}}}$

For a sphere, $\frac{I}{m r^{2}} = \frac{2}{5}$

Hence, $a = \frac{5}{7} g \sin θ = c o n s \tan t$ .

Hence, speed of all spheres is same at the bottom. Sphere (ii) has the largest mass. Hence, it will have the maximum kinetic energy of translation .

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