A

Step 1: Understand the situation. There are 100 identical sliders, all at rest except slider 1, which moves with velocity v.
Step 2: Use conservation of momentum. Before the collision, only slider 1 has momentum, given by \(P_{initial} = m v\), where \(m\) is the mass of one slider.
Step 3: After the collision, all sliders are stuck together and move with a common velocity \(V_f\). The total mass after collision is \(100m\). Therefore, momentum after collision is \(P_{final} = (100m) V_f\).
Step 4: Setting initial momentum equal to final momentum:
\(m v = (100m) V_f\)
Step 5: Cancelling mass \(m\) from both sides gives:
\(v = 100 V_f\).
Step 6: Rearranging gives: \(V_f = \frac{v}{100}\). Thus the correct answer is option A.