A solid sphere of mass \(2\,\text{kg}\) is at rest inside a cube as shown in the figure. The cube moves with velocity
\[
\vec v=(5t\,\hat i+2t\,\hat j)\,\text{ms}^{-1},
\]
where \(t\) is time in seconds. If the sphere is at rest with respect to the cube, find the force exerted by the sphere on the cube. (All surfaces are smooth and \(g=10\,\text{ms}^{-2}\)).
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When an object remains at rest relative to an accelerating container, it must have the same acceleration as the container. Apply Newton's second law separately along each direction and then combine the normal reactions vectorially.
