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A cart loaded with sand moving with velocity $v$. Sand is falling through the hole as shown in diagram then after falling on the ground sand is
Moving with cart
Moving in opposite direction with speed $v$
Stationary on the ground
Moving with speed $v_1$
Solution
(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.
