AP EAMCET Engineering 22 Sep 2020 Shift 1 Paper

Length of pendulum =1
Centre of gravity of pendulum's string =‌

l

2

When pendulum is displaced through 90∘ and released, then according to law of conservation of energy.
Gravitational potential energy = Kinetic energy
⇒‌‌mg⋅‌

l

2

=‌

1

2

mv2⇒v2=gl
⇒‌‌v=√gl...(i)
At the mean position, tension in the string is balanced by the weight as well as the centrifugal force.
Hence, ‌‌T=mg+‌

mv2

l∕2

‌‌[∵r=‌

l

2

]
=mg+‌

2m

1

⋅v2
=mg+‌

2m

l

⋅(√g)2 [from Eq. (i)]
=mg+‌

2mgl

l

=mg+2mg=3mg