Find g from a pendulum.

g is found from a simple pendulum using g = 4π²L/T². The length L is measured with a 1% error and the period T with a 2% error. The maximum percentage error in g is:

Answer: 5%.

For a quantity built from powers, the maximum relative error is the sum of each relative error multiplied by the size of its power, whatever the power's sign. Here g goes as L to the first power and as T to the minus second power.

\frac{Δ g}{g} = \frac{Δ L}{L} + 2 \frac{Δ T}{T} = 1 % + 2 \times 2 % = 5 %

The maximum error in g is 5%. The period's error counts twice because T is squared, and errors always add, even though T sits in the denominator. Forgetting the power gives 3%.

Original practice question · JEE Physics Decoded

What is Level 2?

One step past the obvious.

Every Level 2 starts from a quick question, Level 1, and changes one thing. Seeing what that change does is the skill JEE Main tests. Try it here, free and with no signup, then read the worked answer.

Practise more like this, free Continue practising All Level 2 questions

Free account · Students 15+ in India · Parent approval under 18

Get the Android app on Google Play → (opens in a new tab)

Keep going

Practise more like this, free.

Tests marked like the real exam, and a worked explanation for every question.

Start practising free

Find g from a pendulum.

One step past the obvious.

More Level 2 questions

Practise more like this, free.