A point mass ' m ' attached at one end of a massless, inextensible string of length ' ' performs a vertical circular motion and the string rotates in vertical plane, as shown in the diagram. The increase in the centripetal acceleration of the point mass when it moves from point A to point C is [ g = acceleration due to gravity.]

Step-by-step solution

The centripetal acceleration at any point on the circular path of radius is given by a_c = v^2 , where v is the speed at that point. Applying conservation of mechanical energy between point A (height above the reference level at C) and point C: 1 2 mv_A^2 + mg = 1 2 mv_C^2 Multiplying through by 2 m yields: v_A^2 + 2g = v_C^2 The increase in centripetal acceleration from A to C is: a_c = v_C^2 - v_A^2 = (v_A^2 + 2g ) - v_A^2 = 2g Final Answer: 2g