CBSE Class 11-science Answered
4 identicle bodies of mass m are located at vertices of square of side l they revolve under the effect of mutual gravitational force in circle circumscribing the square then the speed of each body will be
Asked by shivanipanchal6883 | 05 Jan, 2023, 14:44: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/fbd581782e13a421a9f10f33486eb8cf63b6b3c8dd5dd9.12759470g5.png)
Figure shows system that consists of 4 partcles of mass m positioned at the vertex of square of side l .
Each mass is attracted along sides by force FS and also along diagonal by force FD .
Force FS = ![begin mathsize 14px style G space m squared over l squared end style](https://images.topperlearning.com/topper/tinymce/cache/2f3be2f4ac43244fb2d83d195c699f32.png)
![begin mathsize 14px style G space m squared over l squared end style](https://images.topperlearning.com/topper/tinymce/cache/2f3be2f4ac43244fb2d83d195c699f32.png)
Force FD = ![begin mathsize 14px style G space m squared over open parentheses square root of 2 l close parentheses squared space equals 1 half space cross times fraction numerator G m squared over denominator space l squared end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/ea52f1599c0e8042ae23ec80e5a679ae.png)
![begin mathsize 14px style G space m squared over open parentheses square root of 2 l close parentheses squared space equals 1 half space cross times fraction numerator G m squared over denominator space l squared end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/ea52f1599c0e8042ae23ec80e5a679ae.png)
where G is universal gravitational constant.
Forces acting on sides gives resultant along diagonal .
Hence net resultant force Fnet acting on each mass along diagonal is
Fnet = √2 FS + FD = ![begin mathsize 14px style G space m squared over l squared open parentheses square root of 2 space plus space 1 half close parentheses space equals space 1.914 space G space m squared over l squared end style](https://images.topperlearning.com/topper/tinymce/cache/a5555aa6283499f1d4fb410ba7cec44f.png)
![begin mathsize 14px style G space m squared over l squared open parentheses square root of 2 space plus space 1 half close parentheses space equals space 1.914 space G space m squared over l squared end style](https://images.topperlearning.com/topper/tinymce/cache/a5555aa6283499f1d4fb410ba7cec44f.png)
If above force is acting as centripetal force for the masses to rotate along circle
that is circumscribing the square , then speed v of each mass is determined as follows
![begin mathsize 14px style 1.914 space G space m squared over l squared space equals space m space v squared over R end style](https://images.topperlearning.com/topper/tinymce/cache/d8f8decbaa56de737a1eb568cd8c8dac.png)
where R =
is radius of circle
![begin mathsize 14px style 1 half open parentheses square root of 2 space l close parentheses space equals space fraction numerator l over denominator square root of 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/a8ef8522eed52cbb05469469379623bc.png)
![begin mathsize 14px style 1.914 space G space m squared over l squared space equals space m space v squared over l cross times square root of 2 end style](https://images.topperlearning.com/topper/tinymce/cache/9fc8f2351d0dca6e2c30f979f7ac5342.png)
After simplification of above expression, we get ![begin mathsize 14px style v space equals space square root of 1.354 space fraction numerator G space m over denominator l end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/84c07c92d517bf9d88cf33fd10b3ef83.png)
![begin mathsize 14px style v space equals space square root of 1.354 space fraction numerator G space m over denominator l end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/84c07c92d517bf9d88cf33fd10b3ef83.png)
Answered by Thiyagarajan K | 05 Jan, 2023, 17:32: PM
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