A ball of rolls down an inclined plane and acquires a velocity  when it reaches the bottom of the plane. If the same ball slides without friction and aquires rolling from the same height down an equally inclined smooth plane and aquires a velocity (then which of the following statements are not correct?
a)	because a work is done by the rolling ball against the frictional force
b)	because the angular velocity acquired makes the rolling ball to travel faster
c)	because kinetic energy of the two balls is same at the bottom of the planes
d)	because the rolling balls acquires rotational as well as translational kinetic energy

(a,b,c)

When the ball move along a smooth plane, the accelerating force on it is . Hence, its acceleration is equal to

When the ball rolls down the rough inclined plane, then  acts down the plane but a friction comes into existence which acts up the plane. That friction produces angules acceleration on the ball and the net accelerating force on the ball becomes equal to ( friction). Therefore, it has a smaller acceleration. Therefore, its velocity at the bottom of the plane is less than that of the ball moving down a smooth plane or

In fact, at the bottom of the planes both the balls have the same KE because loss of potential energy of both the balls is the same. But the ball rolling down a rough plane has translation as well as rotational kinetic energy at the bottom of the plane while ball sliding down a smooth plane has translational KE only. Therefore, translational KE of the rolling ball will be less than the translational KE of the ball sliding down the smooth plane. Hence, option (d) is correct