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A particle is moving in a vertical i...

A particle is moving in a vertical in a vertical circle . The tensions in the string when passing through two positions at angles `30^(@) and 60^(@)` from the lowest positon are `T_(1) and T_(2)` respectively , then

A

`T _(1) gt T_(2)`

B

`T_(1) lt T_(2)`

C

`T_(1)= T_(2)`

D

Tension in the string always remain the same

Text Solution

Verified by Experts

The correct Answer is:
A
Tension at any point is ` T= (mv^2)/(r ) + mg cos theta `
` therefore T_1 =(mv^2)/(r ) + mg cos 30 ^(@) "for" theta = 30 ^(@)`
`T_(2) = (mv^2)/(r ) + mg cos 60^(@) "for " theta = 60 ^(@)`
`therefore T_1 gt T_2`
[Note : As ` theta ` is increased , ` cos theta ` is decreased Similarly we know that there is maximum tension at the lowest point and then it starts decreasing till it reaches the highest point ]
Thus `t_1gt T_2`
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