Animated Solution for Physics - Laws of Motion: Assertion It is easier to pull a heavy object than to push it on a level ground. Reason The magnitude of frictional force depends on the nature of the two surfaces in contact.

Have you ever tried to move a heavy piece of furniture across the room? You probably noticed that grabbing it from the front and pulling it is significantly less exhausting than getting behind it and pushing. But why? Is it just a psychological trick, or is there a fundamental law of physics at play?

In this classic JEE Assertion-Reason problem, we are challenged to mathematically prove why pulling is easier than pushing, and to evaluate whether the nature of the surfaces is the true reason behind this phenomenon.

Imagine a heavy block of mass $m$ resting on a rough horizontal floor. You attach a rope to it and pull with a force $F$ at an angle $\theta$ above the horizontal.

To understand what happens, we must resolve this pulling force into its rectangular components. The force $F$ splits into: 1. A horizontal component, $F\cos \theta$, which is responsible for dragging the block forward. 2. A vertical component, $F\sin \theta$, which acts upwards, effectively trying to lift the block off the ground.

Because the block is not flying into the air or sinking into the ground, the forces in the vertical direction must be perfectly balanced. The downward force is the weight of the block, $mg$. The upward forces are the normal reaction from the ground, $N_1$, and the vertical component of your pull, $F\sin \theta$.

Equating these gives us the vertical equilibrium equation:

Rearranging for the normal reaction, we get:

This is the crucial moment of insight! By pulling at an upward angle, you are effectively reducing the normal reaction. The ground doesn't have to push up as hard because your upward pull is helping support the block's weight.

Since kinetic friction is directly proportional to the normal reaction ($f_k=\mu N$), the friction experienced while pulling is:

Now, let's reverse the scenario. You get behind the block and push it with the same force $F$, but this time, your force is directed at an angle $\theta$ below the horizontal.

Resolving the pushing force yields: 1. A horizontal component, $F\cos \theta$, pushing the block forward. 2. A vertical component, $F\sin \theta$, which now acts downwards, driving the block harder into the floor.

Let's look at the vertical equilibrium again. The downward forces are now the weight $mg$ AND the vertical component of your push $F\sin \theta$. The only upward force is the normal reaction $N_2$.

By pushing downwards, you have artificially increased the normal reaction. The ground must push back with greater force to support both the block's weight and your downward push.

Consequently, the friction experienced while pushing becomes:

Assertion vs. Reason

Comparing the two frictional forces, it is mathematically obvious that $f_2>f_1$. Pushing generates a significantly larger opposing frictional force than pulling. Therefore, you have to work much harder to maintain the same horizontal motion. The Assertion is absolutely TRUE.

Now, let's evaluate the Reason, which states: "The magnitude of frictional force depends on the nature of the two surfaces in contact."

This statement is the very definition of the coefficient of friction, $\mu$. Whether you are on ice ($\mu \approx 0.05$) or rubber on concrete ($\mu \approx 0.8$), the nature of the surfaces dictates the baseline friction. Therefore, the Reason is also TRUE.

But here is the ultimate trap: Does the Reason explain the Assertion?

Absolutely not! The reason pulling is easier than pushing has nothing to do with the nature of the surfaces. The coefficient of friction $\mu$ remains exactly the same in both scenarios. The true explanation lies in the alteration of the Normal Reaction due to the vertical component of the applied force.

Thus, both statements are true, but the Reason is not the correct explanation for the Assertion. The correct option is (b).