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CBSE Class 12-science Answered

Question 15.
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Asked by ritikabehera01 | 19 Feb, 2019, 10:41: PM
answered-by-expert Expert Answer
begin mathsize 12px style I space equals space integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator d x over denominator 3 plus 2 sin x plus cos x end fraction u s e space s u b s t i t u t i o n space t space equals space tan open parentheses x over 2 close parentheses space space space space h e n c e space d x space equals space fraction numerator 2 d t over denominator 1 plus t squared end fraction space comma space sin x space equals fraction numerator 2 t over denominator 1 plus t squared end fraction comma space cos x space equals space fraction numerator 1 minus t squared over denominator 1 plus t squared end fraction l i m i t s comma space space w h e n space x equals 0 comma space t equals 0 space space semicolon space space w h e n space x equals straight pi divided by 2 space space space comma space straight t space equals space 1 U sin g space t h e space a b o v e space s u b s t i t u t i o n space a n d space a f t e r space s i m p l i f i c a t i o n I space equals space integral subscript 0 superscript 1 fraction numerator open parentheses 1 plus t squared close parentheses d t over denominator t squared plus 2 t plus 2 end fraction w e space n e e d space t o space w r i t e space left parenthesis 1 plus t squared right parenthesis space space space a s comma space space space space 1 plus t squared space equals space A open parentheses t squared plus 2 t plus 2 close parentheses space plus space B left parenthesis 2 t plus 2 right parenthesis space plus space C c o m p a r i n g space c o e f f i c i e n t s comma space w e space g e t space A space equals space 1 comma space B equals negative 1 space a n d space C space equals space 1 H e n c e space I space equals integral subscript 0 superscript 1 d t space minus space integral subscript 0 superscript 1 fraction numerator open parentheses 2 t plus 1 close parentheses d t over denominator t squared plus 2 t plus 2 end fraction space plus integral subscript 0 superscript 1 fraction numerator d t over denominator open parentheses t plus 1 close parentheses squared plus 1 end fraction end style
Above integrals are standard  integrals. Hence further steps can be worked out by the user
Answered by Thiyagarajan K | 20 Feb, 2019, 09:01: AM

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CBSE 12-science - Physics
A dumbbell consists of two masses A and B each of mass m joined by a light rod of length l with mass B attached to a suspension point O by a light rod of length l as shown in figure. Find the minimum required speed with which mass A to be projected horizontally so that the system completes the vertical circular motion.
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