Question icon
Grade 10Mechanics

Two identical uniform frictionless spheres, each of weight W, rest as shown in Fig. at the bottom of a fixed, rectangular container. The line of centers of the spheres makes an angle 0 with the horizontal. Find the forces exerted on the spheres (a) by the container bottom, (b) by the container sides, and (c) by one another
src=data:image/png;base64,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

Profile image of Hrishant Goswami
11 Years agoGrade 10
Answers icon

1 Answer

Profile image of Jitender Pal
11 Years ago
235-146_1.PNG
Therefore, the reaction force from the bottom of the container is 2W .
(b) The sphere at the top is in vertical equilibrium, therefore
235-2086_1.PNG
235-2001_1.PNG
(c) The sphere at the top is in vertical equilibrium, therefore235-2157_1.PNG