AP EAPCET 06-Jul-2022 Shift 2 Paper

The given situation is shown in the figure
At highest point A,
vA=√7gr
TA and TB are tensions in the string when particle is at highest position (A) and lowest position (B). ∴ At point A,At highest point A,
‌‌

mvA2

r

‌=TA+mg
⇒‌‌

m(√7gr)2

r

‌=TA+mg
⇒‌7mg‌=TA+mg
⇒TA‌=6mg
At point B by the law of conservation of energy, change in potential energy = Change in kinetic energy
‌mg(2r)=‌

1

2

mvB2−‌

1

2

mvA2
⇒‌‌2mgr=‌

1

2

mvB2−‌

1

2

m(7gr)
⇒‌‌4gr=vB2−7gr
⇒‌‌vB=√11gr
At lowest point B,TB−‌

mvB2

r

=mg
TB−‌

m

r

⋅11gr‌=mg
⇒‌‌TB−11mg‌=mg
⇒‌‌TB‌=12mg
‌

TA

TB

‌=‌

6mg

12mg

=‌

1

2

⇒‌‌TA:TB‌=1:2