A solid sphere of mass 2 kg is resting inside a cube as shown in fig. The cube is moving with a velocity `vec(v)=(5t hat(i)+2t hat(j))ms^(-1)`. Here t is time in seconds. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube?

Explanation

As given, `vec(v)=5t hat(i)+2t hat(j)` ,
`therefore a_(x)=(dv_(x))/(dt)=5, a_(y)=(dv_(y))/(dt)=2`

When cube is moving with above accelerations along x and y - axes, the forces that exert on cube are
`F_(x)=-ma_(x)=-2xx5=-10N`
`F_(y)=-(mg+ma_(y))=-(20+2xx2)=-24 N`
Net force, `F=sqrt((F_(x))^(2)+(F_(y))^(2))`
`=sqrt((10)^(2)+(24)^(2))=26 N`