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A small bob tied at one end of a thin st...

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 height position is ____ m/s. (Take `g=10m//s^(2))`

Text Solution

Verified by Experts

The correct Answer is:
5
By conservation of energy
`v_("min")^(2) = v^(2) - 4gl` . . . (i)
` T_("max") = mg + ( mv^(2))/( l) ` . . . (ii)
`T_("min") = ( mv_("min")^(2) )/( l) - mg ` . . . (iii)
From equation (i) and (iii)
`T_("min") = (m)/(l) ( v^(2) - 4 gl) - mg`
`(T_("max"))/(T_("min")) = (( v^(2))/(l)+ g)/((v^(2))/(l) - 5 g) rArr (5)/(1) = (( v^(2))/( 1) + 10)/( (v^(2))/(1) - 50) `
`5 v^(2) - 250 = v^(2) + 10`
`v^(2) = 65 ` . . . (iv)
From equation (iv) and (i)
`v_("min") ^(2) = 65 - 40 = 25`
`v_("min") = 5 m//s `
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