Using a simple pendulum, plot its L-T2 graph and use it to find the effective length of second's pendulum.
A simple pendulum consists of a heavy metallic (brass) sphere with a hook (bob) suspended from a rigid stand, with clamp by a weightless inextensible and perfectly flexible thread through a slit cork, capable of oscillating in a single plane, without any friction, with a small amplitude (less than 150) as shown in figure 6.1 (a). There is no ideal simple pendulum. In practice, we make a simple pendulum by tying a metallic spherical bob to a fine cotton stitching thread.
The spherical bob may be regarded by as a point mass at its centre G. The distance between the point of suspension S and the centre G of the spherical bob is to be regarded as the effective length of the pendulum as shown in figure 6.1 (b). The effective length of a simple pendulum, L = l + h + r. Where l is the length of the thread, h is length of hook, r is radius of bob.
The simple pendulum produces Simple Harmonic Motion (SHM) as the acceleration of the pendulum bob is directly proportional to its displacement from the mean position and is always directed towards it. The time period (T) of a simple pendulum for oscillations of small amplitude, is given by the relation,
T = 2 π √ (L/g)
Where, g = value of acceleration due to gravity and L is the effective length of the pendulum.
T2 = (4π2/g) X L or T2 = KL (K= constant)
and, g = 4π2(L/T2)
If T is plotted along the Y-axis and L along the X-axis, we should get a parabola. If T2 is plotted along the Y- axis and L along the X-axis, we should get a straight line passing through the origin.
Vernier constant of the vernier callipers, V.C. = ______________ cm
Zero error, ±e = _____________cm
Diameter of the bob and length of hook
Observe diameter of the bob:= (i) ______cm, (ii)________cm, (iii)___________cm
Mean diameter of bob, d0 = _________cm
Mean corrected diameter of bob, d = d0 ±e = __________cm
Radius of the bob, r = d/2= ____________ cm
Length of the hook, h= __________cm
Standard value acceleration due to gravity, g1 : 980 cm s-2
Least count of stop clock = ____________s
Zero error of stop clock = ___________s
Table 6.1 Determination of time-periods for different lengths of the pendulum.
Mean = L/T2 = _______________________
We know, T = 2 π √ (L/g)
Experimental value, g1 = 4π2(L/T2) = ______________________
So, %error = (g-g1)/g *100 = ______________________
L vs T graph
Plot the graph between L and T from the observations recorded in the table 6.1. Take L along X-axis and T along Y-axis. The L-T curve is a parabola. As shown in the figure 6.2. The origin need not be (0,0) point.
L vs T2 Graph
Plot the graph between L and T2 from the observations recorded in the table 6.1. Take L along X-axis and T2 along Y-axis. The L-T curve is a straight line passing through the (0, 0) point. So the origin of the graph should be chosen (0, 0). As shown in the figure 6.3.
Determination of length of a seconds pendulum from graph:
A second pendulum has time-period 2 s. To find the corresponding length of the pendulum from the L-T graph, draw a line parallel to the L-axis from the point Q1 (0, 2). The line interval the curve L-T at P1. So, the coordinates of P1 is (102, 2).
Length of the seconds pendulum is _____________(102) cm.
To find the length from the L-T2 curve, we, similarly, draw a line parallel to L-axis is form a point Q2 (0, 4). The line intersects the curve at P2. P2 has coordinates (100, 4).
Length of the seconds pendulum is _______________(100) cm.
you may download Simple Pendulum Experiment Class 11 practical manual .pdf Download Now
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