An unloaded bus and a loaded bus are both moving with the same kinetic energy. The mass of the latter is twice that of the former. Brakes are applied to both, so as to exert equal retarding force. If x1 and x2 be the distance covered by the two buses respectively before coming to a stop, then

The correct option is x₁=x₂.

To understand why this is correct, we can apply the Work-Energy Theorem. This theorem states that the net work done on an object by the forces acting on it is equal to the change in its kinetic energy.

$$W=\Delta KE$$

Here, the work done $W$ by a constant retarding force $F$ to stop a vehicle over a distance $x$ is given by:

$$W=F\times x$$

Since both buses are brought to a complete stop, their final kinetic energy is zero, meaning the change in kinetic energy is equal to their initial kinetic energy ($KE$):

$$F\times x=KE$$

Solving for the stopping distance $x$, we get:

$$x=\frac{KE}{F}$$

From this relation, we can see that the stopping distance $x$ depends solely on the initial kinetic energy ($KE$) and the retarding force ($F$). It is completely independent of the mass of the bus.

Since both buses are moving with the same initial kinetic energy and are subjected to the same retarding force, we have:

$$x_1=\frac{KE}{F}=x_2$$

Therefore, both buses cover the exact same distance before coming to a stop, which gives x₁ = x₂.