Using a simple pendulum experiment g is determind by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T ?

Solution

Physics sir · 4 steps

Square the period formula and flip it: 1/T² turns out to be proportional to 1/L, not to L.

1. Start from T. For a simple pendulum, T = 2π√(L/g). Squaring both sides gives T² = 4π² L/g.

   1/T² = g/4π²·1/L

2. Read the shape. Here g/4π² is a constant, so 1/T² × L stays the same for every length. That is a rectangular hyperbola. The graph falls steeply at small L, then flattens out and gets closer and closer to the L-axis.
3. Check the options. Graph (b) falls slowly first and then faster, which is the wrong curvature. Graph (c) rises, but 1/T² must go down as L grows. Graph (d) is a straight line, but 1/L is not linear in L.
4. So. Only graph (a) has the hyperbola shape: steep drop first, then a slow flattening. The answer is (a).

The idea to keep. Before matching a graph, rewrite the formula in terms of the plotted axes. If the product of the two quantities is constant, expect a hyperbola. A straight line needs a linear relation.

Answer from the NTA final answer key. Solution by PrepWiser.