A mass of 0.2kg is whirled in a horizontal circle of radius 0.5m by a string inclined at 30° to the vertical. Calculate the tension in the string and the speed of the mass in the horizontal circle?

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Answer 1 · 2018-07-28T09:20:55

The tension is $=2.26N$ and the speed is $=1.68ms^-1$

Let the tension in the string be $=T (N)$

Then,

Resolving in the vertical direction

$Tcostheta=mg$

The acceleration due to gravity is $=9.8ms^-2$

$T*cos30º=0.2*9.8$

$T=(0.2*9.8)/(cos30)=2.26N$

Resolving in the horizontal direction

$Tsintheta=mv^2/r$

Therefore,

$v^2=(rTsintheta)/(m)$

$v=sqrt((rTsintheta)/(m))$

$=sqrt((0.5*2.26*sin30)/0.2)$

$=1.68ms^-1$