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*Question* :- Find the Centre of Mass of the system → From a solid sphere of radius r having uniform density , a small sphere of radius r/2 is cut at a distance of r/2 from the centre
*Question* :-Find the Centre of Mass of the system →From a solid sphere of radius r having uniform density , a small sphere of radius r/2 is cut at a distance of r/2 from the centre


2 years ago

Khimraj
3007 Points
							 Let the mass of bigger sphere be M with rafius R. Then the mass of smaller sphere with radius R/2 is M/8.Let the centre of the big sphere which is its centre of mass be the origin O. Then the centre of mass of the small sphere is at a distance R/2 from O.When the small sphere is cut out, let the C.M. of the remaining portion shifts to P. Mass of remaining portion = 7M/8.From conservation of centre of mass : C.M. of remaining portion = C.M. of big sphere + C.M. of the small sphere.=> $\dpi{120} \frac{7M}{8}*(-OP) = M*0 + \frac{M}{8}*\frac{R}{2}$=> OP = $\dpi{120} -\frac{R}{14}$So, the centre of mass of the remaining portion shifts to $\dpi{120} \frac{R}{14}$ from tge centre of the circle.Hope it clears.

2 years ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions