A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position i s _____ m/s. (Take g = 10 m/s²)
Physics · Work , Power and Energy · vertical circular motion
JEE Mains 2021

Question

A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position i s _____ m/s. (Take g = 10 m/s²)

Physics · Work , Power and Energy · vertical circular motion

JEE Mains 2021

G1 Physics · Accepted Answer

Let x=v(top)²/(gL). Then T(min)=mg(x-1). By energy, v(bottom)²=v(top)²+4gL, so T(max)=mg(x+5). Given (x+5)/(x-1)=5, x=2.5. Thus v(top)=√(2.5gL)=√25=5 m/s.