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Two blocks of masses 10 kg and 30 kg are placed on x - aixs. The first mass is moved on the axis by a distance of 2 cm right. By what distance should the second mass be moved to keep the position of centre of mass unchanged.

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :mass of the first block, `m_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)=10 kg`<br/>mass of the second block, `m_(2)=30 kg`<br/>Let `x_(1)` and `x._(1)` are positions of `m_(1)`<br/>`x_(1)` and `x._(1)` are positions of `m_(2)`<br/> <a href="https://interviewquestions.tuteehub.com/tag/initially-516121" style="font-weight:bold;" target="_blank" title="Click to know more about INITIALLY">INITIALLY</a> and later respectively<br/><img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XI_V01_B_C07_SLV_005_S01.png" width="80%"/><br/> In this case of `.x_(cm).` is the <a href="https://interviewquestions.tuteehub.com/tag/position-1159826" style="font-weight:bold;" target="_blank" title="Click to know more about POSITION">POSITION</a> of centre of centre of mass then `x_(cm)=(m_(1)x_(1)+m_(2)+x_(2))/(m_(1)+m_(2))`<br/> then the new position of CM when blocks are shifted `x._(cm)=(m_(1)x._(1)+m_(2)x._(2))/(m_(1)+m_(2))`<br/>subtracting the above equations<br/>`x._(cm)-x_(cm)=(m_(1)(x_(1).-x_(1))+m_(2)(x._(2)-x_(2)))/(m_(1)+m_(2))`<br/>`Delta x_(cm)=(m_(1)Delta x_(1)+m_(2)Delta x_(2))/(m_(1)+m_(2))`<br/>`0=(10xx2+30 Delta x_(2))/(40) "" therefore Delta x_(2)=-2//3`<br/>Therefore the second block should be moved left through a distance of 2/3 cm to keep the position of centre of mass <a href="https://interviewquestions.tuteehub.com/tag/unchanged-2316761" style="font-weight:bold;" target="_blank" title="Click to know more about UNCHANGED">UNCHANGED</a>.</body></html>


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