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#