A body of mass 100g moving with a velocity of 10 ms^ -1 collides with a wall. If after collision it moves with…

Analyze the question

A 100 g body hits a wall at 10 m/s and rebounds at 2.0 m/s in the opposite direction. We need the change in momentum.

Concept

Momentum is p = mv, and it is a vector, so direction matters. Change in momentum = final momentum − initial momentum = mv₂ − mv₁

Solution

• Mass: m = 100 g = 0.1 kg (always convert to kg)
• Take the initial direction as positive: • Initial velocity u = +10 m/s • Final velocity v = −2 m/s (opposite direction)

Δp = m(v − u) Δp = 0.1 × (−2 − 10) Δp = 0.1 × (−12) Δp = −1.2 Ns

The magnitude of the change in momentum is 1.2 Ns. The negative sign only shows that the change is directed opposite to the original motion (towards the direction the body rebounds).

Check against the options

Common mistakes

• Using 100 instead of 0.1 kg gives 1200 Ns, which is not an option.
• Subtracting the speeds without the sign change (10 − 2 = 8) gives 0.8 Ns, which is option A. That is the trap, because the body reverses direction.

Tip

When a body rebounds, the velocities add in magnitude: Δp = m(u + v). Here, 0.1 × (10 + 2) = 1.2 Ns. Also always convert grams to kilograms before calculating.