Question

A Question from DCP mechanics:-

A stone of mass 1 kg is tied with a string and it is whirled in vertical circle of radius 1 m.

If tension at the highest point is 50 N then velocity at lowemost point will be?

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Answer 1

Answer:-

Tension=50N.

Formula:-

$t = \frac{m {u}^{2} }{l} + mg(3 \cos( \alpha ) - 2)$

$l = 2r = 2 \times 1 = 2$

t is tension.

substituting the values,

$t = (1) \frac{ {u}^{2} }{2} + 1 \times 10 \: ( - 3 - 2)$

At highest point alpha is equal to 180 degrees

cos 180= -1.

$50 = \frac{ {u}^{2} }{2} - 50$

$\frac{ {u}^{2} }{2 } = 100$

${u}^{2} = 200$

$u = \sqrt{200}$

$u = 10 \sqrt{2}$

$u = 10 \times 1.414$

$u = 14.14 \: \frac{m}{s}$

so,the initial velocity of the particle is 14.14m/s or

$10 \sqrt{2}$

Answer 2

Answer:

Explanation:

Please refer the below attachment !