JEE Main 2018 · Physics · Kinematics and Laws of Motion · medium

A small ball tied to a light inextensible string of length r is whirled in a vertical circle. At the highest point the tension in the string is 2mg.…

Single correct option

A small ball tied to a light inextensible string of length

r

is whirled in a vertical circle. At the highest point the tension in the string is

2mg

. The tension at the lowest point is

Show answer and solution

Answer: (C) $8mg$

At the top:

T_{top}+mg=\dfrac{mv_t^2}{r}

with

T_{top}=2mg

, so

v_t^2=3gr

. Energy conservation over the drop of

2r

v_b^2=v_t^2+4gr=7gr

. At the bottom:

T_b-mg=\dfrac{mv_b^2}{r}=7mg

, so

T_b=8mg

. In general the bottom tension exceeds the top tension by

6mg

for any speed, and

2mg+6mg=8mg

confirms the result.

Original question written in the JEE Main 2018 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake