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A stone of mass m is tied to a string an...

A stone of mass `m` is tied to a string and is moved in a vertical circle of radius `r` making `n` revolution per minute. The total tension in the string when the stone is its lowest point is.

A

`m[ g+ 4pi ^(2) r]`

B

`m[g+(pi^(2)n^2 r^(2))/(60)]`

C

`m[g+(pi^(2)n^(2) r)/(900)]`

D

`m[g+n^2r^(2)]`

Text Solution

Verified by Experts

The correct Answer is:
C
When the string is at the lowest point , the tension in the string `T= (mv^2)/(r ) +mg `
The body performs n revolutions / minute `=((n)/(60))rev//s`
` therefore (mv^2)/(r ) = mr omega ^(2) = mr . 4 pi r^(2) ((n)/(60))^(2)= ( pi ^(2) n^(2) m r) /(900)`
`therefore ` From (1) `T=(pi^(2)n^(2)m r) /(900) +mg `
` therefore T=m[g+(pi ^(2)n^(2) r) /(900)]`
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