MHT CET 2021 Physics Solved Paper

(b) Let original length be xcm.
Initial angular velocity be ω.
Elongation, dx=1cm
According to Newton's law F=−kdx=‌

mv2

r

⇒‌‌−kdx=mω2r
Since, r=(x+1) and dx=1cm
Therefore, −k(1)=mω2(x+1)
...(i)
Again angular velocity is doubled and elongation produced is 5cm.
Therefore, −k(5)=m(2ω)2(x+5)
−5k=4mω2(x+5)
From Eq. (i) and Eq. (ii), we get
‌

5k

k

=‌

4mω2(x+5)

mω2(x+1)

⇒‌‌(x+1)5=4(x+5)
⇒‌‌5x+5=4x+20
⇒‌‌5x−4x=20−5
⇒‌‌x=15cm