A body of mass M1 moving with a velocity U collides with a stationary body of mass M2 and both move with a…

Analyze the question: A moving body (mass M1, velocity U) hits a stationary body (mass M2). They stick together and move with a common velocity V. We need V in terms of M1, M2 and U.

Concept: The principle of conservation of linear momentum says that, if no external force acts, the total momentum before a collision equals the total momentum after it.

Total momentum before = Total momentum after

Solution:

Before collision:

• Body 1: M1 × U = M1U
• Body 2: M2 × 0 = 0 (it is stationary)
• Total = M1U

After collision (common velocity V, combined mass M1 + M2):

• Total = (M1 + M2)V

Equating the two:

M1U = (M1 + M2)V

Dividing both sides by (M1 + M2):

V = M1U ÷ (M1 + M2)

Checking the options:

• A: (M1 + M2) ÷ M1U is the inverse form, so it is wrong.
• B and C: they have M1 − M2 in the denominator, which is wrong because the masses add when the bodies move together.
• D: M1U ÷ (M1 + M2) matches our result.
• E: M2U ÷ (M1 + M2) uses the wrong mass in the numerator. M2 is the stationary body and contributes no initial momentum.

Tip: In "stick together" (perfectly inelastic) collisions, always write: M1U1 + M2U2 = (M1 + M2)V Add the masses on the right. If one body is at rest, its term on the left is zero. Also check that the answer's units make sense: momentum divided by total mass gives velocity.