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NCERT Solutions for Class 9th Science Chapter 7 .6.2 Inclined plane — Pause and Ponder

Book page 1327 Updated on2026-09-08

Q9.
Explain why roads on hills are built to wind around in gentle slopes rather than going straight up (Fig. 4.26)?
Answer

A winding hill road is a long inclined plane. It raises a vehicle through the same height h using a much longer path L, so the force the engine must supply along the road is far smaller.

For a slope, mechanical advantage = L / h   (Eq. 7.13)
Force needed along the road, F′ = mg × (h / L)
Winding the road makes L large for the same h → F′ becomes small
Work done against gravity = F′ × L = mgh — the same either way

Suppose a 1500 kg truck must climb a hill 300 m high, g = 10 m s–2:

Work against gravity = mgh = 1500 kg × 10 m s–2 × 300 m = 4 500 000 J
Straight up a 600 m ramp: F′ = 4 500 000 J ÷ 600 m = 7500 N
Along a winding road 6000 m long: F′ = 4 500 000 J ÷ 6000 m = 750 N — one-tenth
Why it happens: the road cannot reduce the energy the truck needs — that is mgh, fixed by the height of the hill. What the gentle slope does is spread that work over ten times the distance, so the force needed at any instant drops to one-tenth. An ordinary engine and ordinary tyre grip can supply 750 N; they could not supply 7500 N.
Two more reasons: on a gentle slope the tyres are less likely to slip, and coming down the brakes have to remove the same mgh over a much longer distance, so they stay cooler and safer.
Q10.
To reach a higher floor, we find climbing an inclined ladder easier in comparison to climbing a vertical ladder (Fig. 7.30). Explain why.
Answer

The sloping ladder is an inclined plane. Each step lifts you through a smaller height, so each push needs a smaller force — and the ladder itself supports part of your weight.

Vertical ladder: every step raises you the full rung spacing
→ each push must supply almost the whole weight mg, using your arms as well as your legs

Inclined ladder of length L reaching height h:
force along the ladder, F′ = mg × (h / L) < mg
Total work done = F′ × L = mgh — the same for both ladders
Why it happens: on a slanting ladder the rungs push back on your feet perpendicular to the ladder, and this normal force carries a share of your weight. You supply only the part of the weight acting along the slope, and you supply it over a longer climb. On a vertical ladder the rungs push straight up but you must also grip and pull to stay on it, so your arms do a large part of the lifting.
Tip: "easier" here means a smaller force at each moment, not less energy. Climbing to a first floor 3 m up costs a 50 kg student mgh = 50 × 10 × 3 = 1500 J on either ladder.
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