Read before you solve · 3 min

Read Pendulum Tension: Use Energy Between the Two Positions

This short read prepares one exact NSEP pattern: pendulum tension at extreme and bottom. Identify the physical condition before calculating.

NSEP · Oscillations · 1 linked question · 100% coverage

Know this first

Pendulum Tension at Extreme and Bottom is the central idea in this question pattern. Identify the condition in the stem before applying the method below.

Study deeper: NCERT Physics · Oscillations

Start with the physical model

Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.

Build the relation

At an extreme position,

v = 0, so Tmin=mg \cos \theta m

At the bottom, energy conservation gives vmax 2=2gl(1-cosθm), and Tmax=mg+mvmax 2/l = mg(3-2cosθm), so A is correct.

Given Tmax = 3Tmin: 3-2c=3c, hence c=cosθm=3/5

Therefore Tmax = 9mg/5 (B)

With l = 2 m, vmax=sqrt[2g(2)(1-3/5)]≈3.96 m s⁻¹ (C). θm=cos-1(3/5)≈0.927 rad, which lies between π/4 and π/3 (D)

All A,B,C,D.

Check before selecting

Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.

OlympIQ exam lens

✓Name the governing law before using a formula.
✓Keep the stated geometry and direction information explicit.
✓Use one unit or limiting-case check.

OlympIQ trap

At the extreme the bob still has gravity's radial component even though its speed is zero.

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