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NCERT Solutions for Class 9th Science Chapter 7 .4.1 Kinetic energy — Pause and Ponder

Book page 1237 Updated on2026-09-08

Q4.
Two objects A and B of mass m and 4 m have the same kinetic energy. What is the ratio of the magnitude of velocities of A and B?
Answer

The ratio is vA : vB = 2 : 1.

K = ½mv2
Given KA = KB
½ × m × vA2 = ½ × 4m × vB2
m cancels: vA2 = 4 vB2
Taking the square root: vA = 2 vB
vA : vB = 2 : 1
Why it happens: kinetic energy depends on mass to the first power but on speed to the second power. To make up for being 4 times lighter, A needs to be only √4 = 2 times faster.
Check it yourself: put numbers in. Let m = 1 kg and vB = 3 m s–1. Then KB = ½ × 4 kg × 9 m2 s–2 = 18 J, and KA = ½ × 1 kg × 62 m2 s–2 = 18 J. They match.
Q5.
Does the kinetic energy of an object which moves with constant velocity change with its position?
Answer

No. Its kinetic energy stays exactly the same wherever it is.

K = ½mv2
The formula contains only m and v — no h, no x, no position of any kind.
Constant velocity → v does not change → K does not change
Why it happens: constant velocity means zero acceleration, so by Newton's first law the net force on the object is zero. Zero net force does zero net work, and by the work–energy theorem zero work means zero change in energy.
Careful: its potential energy can still change if the position change is vertical — but that would need some other force to lift it, and then the motion would not stay at constant velocity under gravity alone. For horizontal motion at constant velocity, both K and U stay unchanged.
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