Chapter 15: Q.76 (page 419)

A $15 c m$ long, $200 g$ rod is pivoted at one end. A $20 g$ ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?

Short Answer

Expert verified

Period $T = 0.487 s e c$

Step by step solution

Given information

Pivot length $l = 15 c m$

mass of pivot $m_{1} = 200 g = 0.2 k g$

mass of ball $m_{2} = 20 g = 0.02 k g$

Explanation

Moment of Inertia of rod about pivot $= \frac{m_{1} l^{2}}{3}$

Moment of Inertia of clay ball about pivot $= m_{2} l^{2}$

Combine moment of inertia of pivot:

$I = (\frac{m_{1}}{3} + m_{2}) l^{2} = (\frac{0.2}{3} + 0.02) {(0.15)}^{2} I = 0.00195 k g m^{2}$

Combined mass role="math" localid="1650048680672" $M = m_{1} + m_{2} = 0.2 + 0.02 = 0.22 k g$

Time period

$T = 2 π \sqrt{\frac{I}{M g l}} = 2 π \sqrt{\frac{0.00195}{0.22 \times 9.81 \times 0.15}} = 0.487 \sec$

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A $15 c m$ long, $200 g$ rod is pivoted at one end. A $20 g$ ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?

Short Answer

Step by step solution

Given information

Explanation

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A 15cmlong, 200grod is pivoted at one end. A 20gball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Thermodynamics

Dynamics

Physical Quantities And Units

Translational Dynamics

Medical Physics

Study anywhere. Anytime. Across all devices.

A $15 c m$ long, $200 g$ rod is pivoted at one end. A $20 g$ ball of clay is stuck on the other end. What is the period if the rod and clay swing as a pendulum?