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Chapter 15: Q.2 (page 414)

A pendulum on Planet X, where the value of gis unknown, oscillates with a period . What is the periodT=2sof this pendulum if:

a. Its mass is doubled? Explain. Note that you do not know the value of m,L,org, so do not assume any specific values. The required analysis involves thinking about ratios.

b. Its length is doubled?

c. Its oscillation amplitude is doubled?

Short Answer

Expert verified

part (a)

a.Time period remains unchanged if the mass is doubled.

part (b)

b.T'is 2.848secwhen the length is doubled.

part (c)

c.Time is not changed when oscillation amplitude is doubled.

Step by step solution

01

Time period of pendulum (part a)

a) Time period of pendulum

T=2蟺Lg

When the mass is doubled, the time period remains the same since the time period is determined solely by the length of the pendulum and gravity.

02

Calculation for time period after doubling the length (part b)

b) T'is the new time period once the length has been doubled.

T'=2蟺2Lg

T'=2蟺Lg2

T'=2sec脳2

T'=2.848sec

03

Changes after Amplitude changed (part c)

c) With changes in oscillation amplitude, the time period remains constant.

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