Question

suppose 'A' is an object moving at great velocity and less mass but 'B' is an object of more mass but moving at low velocity if we collide both which obj will move back more​

Answer 1

Let the mass of A be m and velocity, before and after collision, be U and V respectively. Similarly, let the mass of B be M and velocity, before and after collision, be u and v respectively. The two bodies are assumed to move in the same direction along a straight line.

By law of conservation of linear momentum, we have,

mU + Mu = mV + Mv

i.e., total momentum before collision = total momentum after collision. Then,

m(U - V) = M(v - u) → (1)

Suppose the collision is to be elastic. Then kinetic energy is also conserved. Hence,

(mU²)/2 + (Mu²)/2 = (mV²)/2 + (Mv²)/2

m(U² - V²) = M(v² - u²) → (2)

By solving (1) and (2), we get,

U + V = u + v

v = U + V - u

Then, from (1),

m(U - V) = M(U + V - 2u)

V = [(m - M)U + 2Mu] / (M + m)

Similarly,

v = [(M - m)u + 2mU] / (M + m)

But if m << M and u << U,

V ≈ - U → (3)

v ≈ 0

(3) implies that the object A moves back after collision.

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