Question

Calculate the change in length of a simple pendulum of length 1 m, when its period of oscillation changes from 2 s to 1.5 s.

Answer 1

Time period is given by, $T=2\pi\sqrt{\frac{l}{g}}$

where l = 1m , T = 2. sec

so, 2 = 2π √{1/g} .......(1)


when, T = 1.5 sec then, we have to find length of simple pendulum. e.g., L

1.5 = 2π √{L/g} .......(2)

from equations (1) and (2),

2/1.5 = √{1/g}/√{L/g}

or, 4/3 = √{1/L}

or, 16/9 = 1/L

or, L = 9/16 m

hence, change in length of simple pendulum = 1 - 9/16 = 7/16 = 0.4375 m

Answer 2

Answer:

Explanation:for seconds pendulum T1=2sec

Length l1 =1m

New time period T2 = 1.5sec

Length l2 = ?

T = 2π√l/g

For seconds pendulum,2= 2π√l/g

For new time period,1.5= 2π√l/g

2/1.5=√1/g/√l/g

2/1.5=1/√l

l=9/16m

Therefore decrease in length = 1-9/16 = 7/16m=0.4375m