JEE Class main Answered
In the arrangement shown pullies and strings are ideal. The acceleration of block B is
![question image](https://images.topperlearning.com/topper/new-ate/639743664d622340e202IMG20230811172436.jpg)
Asked by soulful.my.me | 11 Aug, 2023, 17:27: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/32d3fff4559ecbd17d140b357149053a64d71d3797a430.44088399f1.png)
Figure shows the free body diagram of block-B , block-A and of pulley.
In Block-B , (mg) is weight of the block and T is tension force in the rope . Le block-B moves upward with acceleration a.
In Pulley , Tension force in the cable connected to block A becomes 2T because there are two tension forces acting in the
direction opposite to tension force of the cable connected to block-A .
In block-A , (2mg) is weight and N is normal force .
If there is no displacement in vertical direction , then net force along vertical direction is zero.
Hence we get , N - ( 2mg ) = 0 , or normal force N = ( 2mg )
Friction force f = μN , where μ = 0.5 is kinetic friction coefficient .
Hence friction force f = 0.5 * ( 2mg ) = mg
If we apply Newton's second law to the block-B , then we have
![begin mathsize 14px style T space minus space m g space equals space m space a end style](https://images.topperlearning.com/topper/tinymce/cache/25a1ab48b4e8d7052963328c70f52b45.png)
If we apply Newton's second law to the block-A , then we have
![begin mathsize 14px style left parenthesis 4 m g right parenthesis space minus space 2 T space minus space f space equals space left parenthesis 2 m right parenthesis space left parenthesis a divided by 2 right parenthesis end style](https://images.topperlearning.com/topper/tinymce/cache/9541cdab074690e469730b420f0a26c8.png)
By substituting friction force and after simplification , above expression becomes
![begin mathsize 14px style left parenthesis 4 m g right parenthesis space minus space 2 T space minus space left parenthesis m g right parenthesis space equals space m space a end style](https://images.topperlearning.com/topper/tinymce/cache/c2f0a582a310d79b26b58b4c323c8fb9.png)
We can eliminate tesnion force T by multiplying eqn.(1) by 2 and addig to eqn.(2) ,
then we get after simplification
![begin mathsize 14px style g space equals space 3 space a end style](https://images.topperlearning.com/topper/tinymce/cache/4224d49c95fc08df7ad629250857df70.png)
hence acceleration of block-B is , a = (1/3) g
Answered by Thiyagarajan K | 12 Aug, 2023, 11:40: AM
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