Question

Take a 1 m long thread of negligible mass. Consider three spherical/ cuboidal bobs of

same sizes but different masses. Form simple pendulum using thread and bob, and estimate

the time period of each of the pendulum by recording time for 20 oscillation three times

for each pendulum formed. Tabulate the observations taken. Interpret your results and

justify. List your 2 main conclusions derived from the above project.​

Answer 1

Answer:

In the given project all the three spherical/cuboidal bobs of different masses but same sizes will have the same time period.

Explanation:

Second's pendulum: A pendulum that moves from one extreme position to the other in exactly one second. As a result, its time period is exactly 2 seconds.

Simple pendulum: A point mass hung from a rigid point support by an inextensible, mass-less thread. In reality, a small heavy spherical bob of high density material with a radius r much less than the length of the suspension is hung by a light, flexible, and strong string/thread that is securely maintained at the other end by a clamp stand.

• The radius of bob may be found from its measured diameter with the help of callipers by placing the pendulum bob between the two jaws of (a) ordinary callipers, or (b) Vernier Callipers, as described in Experiment E 1.1 (a). It can also be found by placing the spherical bob between two parallel card boards and measuring the spacing (diameter) or distance between them with a metre scale.
• The accuracy of the result for the length of second's pendulum depends mainly on the accuracy in measurement of effective length (using metre scale) and the time period T of the pendulum (using stop-watch). As the time period appears as T 2 a small uncertainty in the measurement of T would result in appreciable error in T2 , thereby significantly affecting the result. A stop-watch with accuracy of 0.1s may be preferred over a less accurate stop-watch/clock.
• Some personal error is always likely to be involved due to stop-watch not being started or stopped exactly at the instant the bob crosses the mean position. Take special care that you start and stop the stop-watch at the instant when pendulum bob just crosses the mean position in the same direction.
• Sometimes air currents may not be completely eliminated. This may result in conical motion of the bob, instead of its motion in vertical plane. The spin or conical motion of the bob may cause a twist in the thread, thereby affecting the time period. Take special care that the bob, when it is taken to one side of the rest position, is released very gently.
• To suspend the bob from the rigid support, use a thin, light, strong,
• unspun cotton thread instead of nylon string. Elasticity of the
• string is likely to cause some error in the effective length of the
• pendulum.
• The simple pendulum swings to and fro in SHM about the mean,
• equilibrium position. Eq. (E 6.1) that expresses the relation between T and L as T = 2 / π L g , holds strictly true for small amplitude or swing θ of the pendulum. Remember that this relation is based on the assumption that sin θ ≈ θ, (expressed in radian) holds only for small angular displacement θ.
• Buoyancy of air and viscous drag due to air slightly increase the time period of the pendulum. The effect can be greatly reduced to a large extent by taking a small, heavy bob of high density material (such as iron/ steel/brass).

Two main conclusions derived from the given project are-

• The time period of all the bobs would be the same.
• Time period will not depend on the mass of bobs as they are suspended from the thread of the same length.
• A hefty point mass (referred to as the "bob") is linked to one end of a string that is perfectly extendable, flexible, and weightless to create the perfect basic pendulum. It hangs from a solid or rigid support.
• A simple pendulum's time period, designated by the letter "T," is the amount of time it takes to complete one complete oscillation.
• The time period for any simple pendulum can be written as,
• T = 2π/ω = 2π × √(L/g)
• Here, T is the time period, g is the gravitational force, and L is the length of the pendulum.
• As we can see from this equation, the time period does not depend on the mass of the bob.
• Hence, in the given project all the three spherical/cuboidal bobs of different masses but same sizes will have the same time period.

Reference Link

• https://brainly.in/question/46953111
• https://brainly.in/question/13823662