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Ques   let A,B,C,D be points on a vertical line such that  AB=BC=CD . if a body is released from position A, the times of descent through AB,BC and CD are in ratio

Asked by Kajalmandal64 11th August 2017, 9:08 PM
Answered by Expert
Answer:
 
The following steps should be followed for solving such queries:
 
1) For part AB: Use third equation of motion to get the relation as begin mathsize 12px style straight d equals 1 half gt subscript 1 superscript 2 rightwards double arrow straight t subscript 1 equals square root of fraction numerator 2 straight d over denominator straight g end fraction end root end style
 
2) Now, take total distance AC. Third equation of motion gives begin mathsize 12px style 2 straight d equals 1 half straight g open parentheses straight t subscript 1 plus straight t subscript 2 close parentheses squared rightwards double arrow straight t subscript 1 plus straight t subscript 2 equals square root of fraction numerator 4 straight d over denominator straight g end fraction end root end style
 
3) Finally for total distance AD: begin mathsize 12px style 3 straight d equals 1 half straight g open parentheses straight t subscript 1 plus straight t subscript 2 plus straight t subscript 3 close parentheses squared rightwards double arrow straight t subscript 1 plus straight t subscript 2 plus straight t subscript 3 equals square root of fraction numerator 6 straight d over denominator straight g end fraction end root end style
 
4) Find t2 and t3 from the equations obtained in steps 2 and 3. Take the ratio with t1. You will get t1:t2:t3begin mathsize 12px style 1 colon open parentheses square root of 2 minus 1 close parentheses colon open parentheses square root of 3 minus square root of 2 close parentheses end stylebegin mathsize 12px style 1 colon open parentheses square root of 2 minus 1 close parentheses colon open parentheses square root of 3 minus square root of 2 close parentheses end style
Answered by Expert 12th August 2017, 12:14 PM
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