A uniform disc rolls without slipping on a rough horizontal surface with uniform angular velocity. Point O is the centre of disc and P is a point on disc as shown. In each situation of column I a statement is given and the corresponding results are given in column II. Match the statements in column-I with the results in column-II.
Column I | Column II |
(i) The velocity of point P on disc | [A] Change in magnitude with time |
(ii) The acceleration of point P on disc | [B] Is always directed that point (the point on given in column -I) towards centre of disc |
(iii) The tangential acceleration of point p on disc | [C] Is always zero |
(iv) The acceleration of point on disc which is in contact with rough horizontal surface | [D] Is non zero and remains constant in magnitude |
Text Solution
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Ans.
(i) [A]
(ii) [B], [D]
(iii) [A]
(iv) [B], [D]
Sol speed of point P changes with time
Acceleration of point P is equal to ω 2 × ( ω = angular speed of disc and X = OP). The acceleration is directed from P towards O.]
The angle between acceleration of P (constant in magnitude) and velocity of P changes with time. Therefore , tangential acceleration of P changes with time.
The acceleration of lowest point is directed towards centre of disc and remains constant with time.
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