Question

You push a small mass (with respect to your mass) crate on a frictionless surface and it has some acceleration. If you are standing on the same frictionless surface, what happens to you?

	a)	You stay where you are.
	b)	You move forward at very low velocity.
	c)	You move backward at very low velocity.
	d)	You move forward at very high velocity.
	e)	You move backward at very high velocity

Answer 1

According to Newton's third law of motion, every action has its equal and opposite reaction. If I push a small mass crate on a frictionless surface and it has some acceleration, the equal amount of force ( magnitude of the force is equal to the force exerted by me on the small mass) is exerted by the small crate on me in the backward direction ( according to Newton's third law of motion). The total linear momentum of the system ( me and the crate) should be conserved ( according to Newton's second law of motion).

If M and m are the mass of my body and the crate respectively and V and v are the velocities of my body and the crate respectively,

M*V + m* v =0

V = (- m / M ) * v

If m < M, V < v which means that my velocity will be less than the crate's velocity.

The negative sign of V signifies that my motion will be in the backward direction.

So, option (c) is correct i.e. I move backward at very low velocity (Ans).