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In a constant , when the bob moves in...

In a constant , when the bob moves in a horizontal circle of radius r, with uniform speed v, the string of length L describes a cone of semivertical angle `theta ` . The tension in the string is given by

A

`T=(mgL)/((L^(2)-r^(2)))`

B

`((L^(2)-r^(2))^(1//2))/(mgL)`

C

`T=(mgL)/(sqrt(L^(2)-r^(2))`

D

`T=(mgL)/((L^(2)-r^(2) )^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

For a contal pendulum , the tension in the string is calculated by using ` T cos theta = mg `
From the figure ` cos theta = (OA) /(OB ) = ( sqrt(L^(2)-r^(2)))/( L )`
` therefore T= ( mg ) /( cos theta ) = ( mg ) /( (sqrt( L^(2)- r^(2)))/(L ))= ( mg L) /( sqrt(L^(2) - r^(2)))`
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