A solid sphere of mass 2kg is resting inside a cube as shown in the figure. V = ( 5 t i ^ + 2 t j ^ ) m / s . Here t is the time in second. All surfaces are smooth. The sphere is at rest with respec

Question

A solid sphere of mass 2kg is resting inside a cube as shown in the figure. $V =$ $(5 t \hat{i} + 2 t \hat{j}) m / s$ . Here t is the time in second. All surfaces are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take $g = 10 m / s^{2}$ & y-axis along vertical)

TestHub · Accepted Answer

The cube has acceleration a = d t d V ​ = ( 5 i ^ + 2 j ^ ​ ) m/ s 2 . The sphere is at rest relative to the cube, so it has the same acceleration. Horizontal: F x ​ = m a x ​ = 2 × 5 = 10 N . Vertical: F y ​ − m g = m a y ​ ⇒ F y ​ = 2 ( 10 ) + 2 ( 2 ) = 24 N . Total force = 1 0 2 + 2 4 2 ​ = 26 N , and by Newton's third law the sphere exerts the same magnitude on the cube.

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