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Question

A ball is dropped from a height of 900 centimetres. Each time it rebounds, it rises to two-third of the height it has fallen through. The total distance travelled by the ball before it comes to rest in metres, is

A
27
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B
36
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C
18
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D
45
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Solution

The correct option is D 45
H=9 metres
Total distance travelled by ball before it comes to rest is
H+2[23H+(23)2H+(23)3H+ upto ]
=H+2H[23+(23)2+(23)3+ upto ]
=H+2H⎜ ⎜ ⎜23123⎟ ⎟ ⎟
=H+4H=5H
=5×9=45 metres

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