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

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Classical Mechanics

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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?