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A toy cart is tied to the end of an...

A toy cart is tied to the end of an unstrectched string of length 'l' when revolved , the toy cart moves in horizontal circle with radius '2l' and time period T. IF it is speeded until it moves in horizontal circle of radius '3l' with period `T_(1) ,` relation between `T and T_(1) ` is (Hooke 's law is obeyed )

A

`T_(1)= (2)/(sqrt3)`

B

`T_(1)= sqrt((3)/(2)) T`

C

`T_(1)= sqrt((2)/(3))T`

D

`T_(1)= (sqrt3)/(2) T`

Text Solution

Verified by Experts

The correct Answer is:
D
`F= m omega^(2) r " " Kl = m ((2pi)/(T))^(2) (2l)` ...(i)
`F_(1)= m omega_(1)^(2) r rArr 2Kl = m ((2pi)/(T_(1)))^(2) (3l)` ....(ii)
On dividing eq. (i) by (ii)
`(Kl)/(2Kl) = (m((2pi)/(T))^(2) (2l))/(m((2pi)/(T_(1)))^(2) (3l))`
`rArr ((T_(1))/(T))^(2)= (3)/(4) rArr T_(1)= (sqrt3)/(2) T`
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