Toy cart tied to the end of an unstretched string of length a, when revolved moves in a horizontal circle of radius 2a with a time period T. Now the toy cart is speeded up until it moves in a horizontal circle of radius 3a with a period T. If Hooke's law (F=kx) holds, then

Options

A. `T_(1)=(2)sqrt(3)T`
B. `T_(1)=sqrt(3)/(2)T`
C. `T_(1)=sqrt(2)/(3)T`
D. `T_(1)=sqrt(3)/(2)T`

Answer

d

Explanation

using `y=(f)/(A Delta i).I` or `Y=(f)/(A).(I)/((2I-I)) rarr F= YA`
the force f will provide required centripetal force for the horizontal circular motion
`F=(mv^(2))/(r )`
and time period `T=(2pir)/(V) rarr T^(2)=(4pi^(2)r^(2))/(V^(2))`
`T^(2)=(4pi^(2)m(2I))/(F)`
time period `T_(1)=(4pi^(2)mr^(2)r)/(F_(1)r)=(4pi^(2)m(3L))/(2yA)`
`T_(1)=sqrt(3)/(2) T`