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Question

A disc arranged in a vertical plane has several grooves directed along the chords drawn from a point A (topmost point) as shown in the figure. Several bodies begin to slide down the respective grooves from A simultaneously. The ratio of their times of slide will be: (neglect friction and air resistance)
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A
AB : AC : AD : AE
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B
1 : 1 : 1 : 1
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C
AE : AD : AC : AB
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D
1 : 2 : 3 : 4
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Solution

The correct option is B 1 : 1 : 1 : 1
Suppose a chord makes an angle θ with the vertical line.
A body constrained to move along this line will experience the component of acceleration due to gravity along this line which is gcosθ.
The length of this chord is 2rcosθ.
In the equation: s=ut+12at2, substituting u =0, s=2rcosθ and a=gcosθ,
We get: 2rcosθ=12gcosθt2
t=4rg
We find that the time is independent of θ.
Hence, the time taken will be same for any chord.
33881_2082_ans.png

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