To avoid slipping while walking on ice, one should take smaller steps because of the

The correct answer is: Friction of ice is small

To understand why taking smaller steps helps avoid slipping on ice, we need to analyze the forces involved in walking using the concept of friction.

How Walking Works — The Role of Friction

When we walk, we push our foot backward against the ground. By Newton's Third Law, the ground pushes our foot forward — this forward push is provided by static friction between our foot and the surface. Without friction, we cannot walk; we would simply slip.

Forces Acting on the Foot During a Step

When we take a step, two key forces act on the foot in contact with the ground:

1. Normal Reaction (N) — acts vertically upward, equal to the component of body weight on that foot.
2. Friction Force (f) — acts horizontally, enabling forward motion.

The maximum static friction available is given by:

f_{\max }=\mu ·N

where μ is the coefficient of static friction and N is the normal force.

Why Ice is Dangerous — Small μ

Ice has an extremely low coefficient of friction (μ is very small, often as low as 0.03–0.1). This means the maximum friction force available is very limited:

f_{\max }=\mu ·N\to \text{very small}

How Step Length Affects the Required Friction

When you take a larger step, your foot lands farther ahead, and your body leans more. This increases the horizontal force component your foot must exert backward against the ground — and therefore requires a larger friction force to keep you from slipping.

When you take a smaller step, your body stays more upright and closer to vertical. The horizontal push of the foot on the ground is smaller, so only a small friction force is needed to prevent slipping:

f_{\mathrm{required}}<f_{\max }=\mu ·N

As long as the required friction stays below the maximum available friction, you will not slip.

Putting It All Together

Since the friction of ice is very small (low μ), the maximum friction force the ice can provide is limited. Taking smaller steps reduces the amount of friction needed to walk safely. This ensures that the required friction remains within the small limit that icy surfaces can provide, thus preventing slipping.

Why the Other Options are Incorrect:

- "Friction of ice is large" — Incorrect. Ice is known for its extremely low friction.
- "Larger normal reaction" — Incorrect. The normal reaction depends on body weight, not step size. Taking smaller steps does not significantly change N.
- "Smaller normal reaction" — Incorrect. Same reasoning as above; step size does not alter the normal force meaningfully.

Conclusion: One should take smaller steps on ice because the friction of ice is small. Smaller steps require less friction to maintain balance, which stays within the low frictional limit that ice can provide.