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CBSE Class 11-science Answered

In the problem no. 34 of concepts of physics HC Verma-1 bit(a) , why is the acceleration of block B is half the acceleration of block A? And why is it that distance travelled by block B is half the distance travelled by block A?
question image
Asked by sakethrockzz007 | 04 Aug, 2023, 23:17: PM
answered-by-expert Expert Answer
Let l1 be the length of rope between the point c and d . Let l2 be the length of the rope between e and f . 
 
Let l3 be the length of rope between a and b .
 
begin mathsize 14px style l subscript 1 space plus space l subscript 2 space plus space l subscript 3 space equals space L space left parenthesis space l e n g t h space o f space r o p e space equals space c o n s tan t space right parenthesis end style
 
If block-A moves down by a distance y , then length of rope between a and b becomes ( l3 + y )
 
Then length of rope between c and f reduces by y because total length is constant .
 
Hence length of rope between c and d reduces by y/2 , similarly length of rope between e and f reduces by y/2 .
 
Hence block-B raises by a distance y/2.
 
Magnitude of displacement yB of block-B is half of magnitude of displacement yA of block-A
 
begin mathsize 14px style y subscript B space equals space 1 half y subscript A end style
Similarly for velocity v
 
begin mathsize 14px style fraction numerator d over denominator d t end fraction y subscript B space equals space 1 half fraction numerator d over denominator d t end fraction y subscript A
v subscript B space equals space 1 half v subscript A end style
 
Similarly for accelerationa
 
begin mathsize 14px style fraction numerator d over denominator d t end fraction v subscript B space equals space 1 half fraction numerator d over denominator d t end fraction v subscript A
a subscript B space equals space 1 half a subscript A end style
Answered by Thiyagarajan K | 07 Aug, 2023, 15:09: PM

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