(i) A solid sphere of radius R is released on a rough horizontal surface with its top point having thrice the velocity of its bottom point A `(V_(A) = V_(0))` as shown in figure. Calculate the linear velocity of the centre of the sphere when it starts pure rolling. (ii) Solid sphere of radius R is placed on a rough horizontal surface with its centre having velocity `V_(0)` towards right and its angular velocity being `omega_(0)` (in anticlockwise sense). Find the required relationship between `V_(0)` and `omega_(0)` so that - (a) the slipping ceases before the sphere loses all its linear momentum. (b) the sphere comes to a permanent rest after some time. (c) the velocity of centre becomes zero before the spinning ceases.

(i) A solid sphere of radius R is released on a rough horizontal surfa

1.	(i) A solid sphere of radius R is released on a rough horizontal surface with its top point having thrice the velocity of its bottom point A `(V_(A) = V_(0))` as shown in figure. Calculate the linear velocity of the centre of the sphere when it starts pure rolling. (ii) Solid sphere of radius R is placed on a rough horizontal surface with its centre having velocity `V_(0)` towards right and its angular velocity being `omega_(0)` (in anticlockwise sense). Find the required relationship between `V_(0)` and `omega_(0)` so that - (a) the slipping ceases before the sphere loses all its linear momentum. (b) the sphere comes to a permanent rest after some time. (c) the velocity of centre becomes zero before the spinning ceases.
Answer» Correct Answer - (i) `(12V_(0))/(7)` (ii) (a) `V_(0) gt (2)/(5) omega_(0) R` (b) `V_(0) = (2)/(5) omega_(0) R` (c) `V_(0) lt (2)/(5) omega_(0) R`

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