A block of mass M is placed on a rough floor of a lift. The coefficient of friction between the block and the floor is μ . When the lift falls freely, the block is pulled horizontally on the floor. What will be the force of friction

The correct answer is None of these. The force of friction acting on the block is zero (0), which is not listed among the other options.

Let us understand this step by step using the concept of free fall and the origin of friction.

Step 1: Understand what "freely falling" means

When a lift (elevator) falls freely, it means the lift is in free fall under gravity alone — there is no support force from cables or any upward reaction. In this situation, every object inside the lift — including the block of mass M — is also falling freely under gravity with the same acceleration g (downward).

Step 2: Find the Normal Force on the block

The friction force between two surfaces depends on the Normal force (N) between them:

f=\mu N

To find N, we apply Newton's second law to the block in the vertical direction. Let upward be positive. The block experiences:

- Weight: Mg downward

- Normal force from the floor: N upward

Since the lift is in free fall, the acceleration of the block is g downward (same as the lift, so there is no relative acceleration between the block and the floor of the lift).

Applying Newton's second law (taking downward as positive):

Mg-N=Mg

N=Mg-Mg=0

The Normal force becomes zero during free fall. This is the well-known condition of "weightlessness" — the block effectively loses its weight as far as the floor of the lift is concerned.

Step 3: Calculate the Friction Force

Since friction depends on the Normal force:

f=\mu N=\mu \times 0=0

The force of friction is zero.

Step 4: Why "None of these" is the correct option

The other options — \mu Mg, \mu Mg/2, and 2\mu Mg — all assume that the Normal force is non-zero (specifically Mg, Mg/2, or 2Mg respectively). These would apply in cases where the lift is stationary, decelerating upward, or accelerating downward at less than g. But during free fall, the Normal force is completely zero, making all of those options incorrect.

The correct answer is that the friction force = 0, which corresponds to "None of these."

Key Takeaway: Friction requires a contact force (Normal force) between surfaces to exist. In free fall, both the lift and the block accelerate equally under gravity, so the block exerts no force on the floor, the floor exerts no Normal force on the block, and consequently there is no friction at all — regardless of how hard the block is pulled horizontally.