NCERT Solutions for Class 9th Science Chapter 7 Chapter opener — Think It Over

Book page 116 Updated on2026-09-08

Q1.

What will be the magnitude of velocity of the child at the bottom of the blue slide?

Answer

If h is the height of the platform above the ground, the child arrives at the bottom with speed v = √(2gh).

At the top: kinetic energy = 0, potential energy = mgh
At the bottom: potential energy = 0, kinetic energy = ½mv²
Conservation of mechanical energy (ignoring friction):
½mv² = mgh
v² = 2gh
v = √(2gh)

For the playground in the picture the deck is about 2 m above the ground, so

v = √(2 × 10 m s^–2 × 2 m) = √(40 m² s^–2) ≈ 6.3 m s^–1

Why it happens: the mass m cancels from both sides, and so does the shape of the slide. Only the vertical drop h decides the speed, because only the vertical drop decides how much gravitational potential energy is converted into kinetic energy.

Q2.

Will two children of different masses reach the bottom of the same slide with the same velocity?

Answer

Yes — both reach the bottom with the same speed, √(2gh).

½mv² = mgh
The mass m appears on both sides and cancels
v = √(2gh) — independent of m

Why it happens: a heavier child does store more potential energy at the top (mgh is larger), but that same larger mass has to be accelerated. The two effects cancel exactly, just as all bodies fall freely with the same acceleration g.

Tip: in real life friction between the child's clothes and the slide does work, and that work depends on how hard the child presses on the surface. So a very light child on a slow, rough slide can arrive a little slower than this ideal answer.

Q3.

Which of the slides will result in the largest magnitude of velocity for the child at its bottom?

Answer

Look at the picture on page 116: the blue spiral slide, the red straight slide and the purple wavy slide all begin at the same platform and end at the same ground. So the vertical drop h is the same for all three, and — ignoring friction — all three give the same speed at the bottom, v = √(2gh).

v = √(2gh) depends only on h
same h → same v, whatever the length or shape of the path

Why it happens: gravity does work only through the vertical drop. Sliding sideways or curling round a spiral adds path length but no extra height, so it adds no extra energy.

Check it yourself: once friction is allowed for, the long blue spiral rubs the child over a much greater length of surface, so it takes away the most energy. In practice the short steep red slide gives the fastest arrival. A slide whose top was higher would beat all three.

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