A point mass ' m ' attached at one end of a massless, inextensible… | MHT CET 2025 (25 Apr, Shift 1)

Q5MHT CET 2025 · 25 APR · SHIFT 1Medium

Critical Speed & Looping

A point mass ' $m$ ' attached at one end of a massless, inextensible string of length ' $l$ ' 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.]

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Answer: (b)

From the figure, A is the top and C is at the level of O, so C is $l$ below A.
Energy: $v_C^2 = v_A^2 + 2gl$
Increase in $a_c = \frac{v_C^2 - v_A^2}{l} = \frac{2gl}{l} = 2g$
So the answer is (b) 2 g.

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