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 (in N) exerted by the sphere on the cube?

Explanation

The velocity of the sphere is same as that of the cube, which is given as `vec(v)=5t hat(i)+2t hat(j)`.
Hence, acceleration of the sphere: `vec(a)=(d vec(v))/(dt)`
or `vec(a)=(5hat(i)-2hat(j))ms^(-2)`
Hence, `a_(x)=5 ms^(-2)` and `a_(y)=2ms^(-2)`
From FBD of sphere `N_(x)=ma_(x) = 2 xx 5 =10 N`
`N_(y)-mg=ma_(y) implies N_(y)= 2 xx 10 + 2 xx 2 = 24 N`
Total force `=sqrt(N_(x)^(2)+N_(y)^(2)) = sqrt((10)^(2)+(24)^(2)) = 26 N`.