Physics · Oscillations · NEET
To the centre. The effective length runs from the fixed point of suspension all the way down to the centre of mass of the bob. So if the string length is l and the bob has radius r, the effective length is L = l + r. A common mistake is to stop at the top of the bob, which gives you only the string length l and a wrong time period.
Because the whole bob oscillates about the point of suspension, and its mass is concentrated at its centre. The restoring torque and the time period depend on the distance from the pivot to the centre of mass, which is (string length + radius). If the bob were a true point mass, r would be zero and L would just equal l. Real bobs have size, so we add r.
Length of string (l) is only the thread from the support to the top of the bob. Effective length (L) is the full distance from the support to the centre of the bob, so L = l + r. Time period uses the effective length: T = 2 pi root(L / g). If a question gives you the string length and the bob radius separately, add them before using the formula.
Time period depends on effective length as T = 2 pi root(L / g). A longer effective length gives a larger time period, because T is proportional to root(L). For example, doubling the effective length multiplies T by root(2), about 1.41 times. Since T depends on root(L), a small radius r adds only a little to T when the string is long.
The geometric effective length L = l + r does not change, but the effective gravity g can change. In a lift accelerating up, g becomes (g + a); accelerating down it becomes (g - a); on a frictionless incline of angle theta it becomes g cos theta. The time period is then T = 2 pi root(L / g_effective). So effective length is about geometry, while effective gravity is about the surroundings.
Savitha, a Class XI student, performs an experiment to find the effective length L of a simple pendulum. She records the time for 30 oscillations as 60 s. The length she calculates is (take pi squared = 9.8 and g = 9.8 m/s squared)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
L = l + r, where l is the length of the string and r is the radius of the bob. The effective length is measured from the point of suspension to the centre of the bob.
Yes. You measure to the centre of the bob, so half the bob's diameter (its radius) is included. If the bob's diameter d is given, add d/2 to the string length.
The effective length L, not just the string length. Using only the string length gives a slightly smaller, incorrect time period.
If the bob is treated as a point mass or its radius is not given, take L equal to the string length l, because r is taken as zero.
