Question #1ad48

2 Answers
Jan 19, 2018

Time period will decrease by 6 %

Explanation:

Suppose,the initial length of the pendulum was 100l and time period was T1

So,we can write,
T1 =2pisqrt(100l/g)

If,length is decreased by 10 %, new length becomes 90l and if time period is now T2# then we can write,

T2 = 2pisqrt(90l/g)

Dividing T2 by T1 we get,
(T2)/(T1) = sqrt(90/100)
Or, (T2)/(T1)=0.94
Or, 1-(T2)/(T1) = 1-0.94
Or, (T1 - T2)/(T1) = 0.06
So, (del T)/(T1) *100 = 6

Jan 19, 2018

See the explanation below

Explanation:

The period of a pendulum of "length"=l is

T=2pisqrt(l/g)

The new length of the pendulum is

L=0.9l

The new period is

T_N=2pisqrt((0.9l)/g)

T_N=(sqrt0.9)2pisqrt(l/g)

T_N=sqrt(0.9)T

The new period is T_N=0.95T