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Question

A body is freely falling under the action of gravity. It covers half the total distance in the last second of its fall. If it falls for n second, then the value of n is

A
2
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B
2+2
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C
2
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D
22
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Solution

The correct option is B 2+2
Let h be the total distance covered in n second then,
for free fall h=12gn2
As per the question, distance covered by it in last second i.e. (n1)th sec is given by
h=h2=12gn22=14gn2
Thus, we have
12g(n1)2=14gn2
Solving above equation we get a quadratic equation in n as
n24n+2=0
n=(4)±(4)24×22
n=4±222=2±2
Now, n1>0 if n=22
(22)1>0 12<0
Hence, the value of n is 2+2.

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