a
(a)

Given :- Velocity of sand loaded cart \(= v\)

To Find :- Direction and speed of sand after falling on ground

Solution :- Let the mass of cart be \(m _1\)

Mass of sand be \(m _2\)

And, Velocity of sand be \(v_2\)

Now, By law of conservation of momentum i.e,

\(\left( m _1+ m _2\right) v = m _1 \times v + m _2 \times v _2\)

\(m _1 v + m _2 v = m _1 v + m _2 v _2\)

\(m _2 v = m _2 v _2\)

\(\therefore v = v _2\)

\(\Rightarrow\) Sand is moving in the same direction and with same speed that of cart

\(\therefore \quad\) Sand is moving with cart

Hence, Option \(A\) (moving with cart) is correct.