Question

A stone of mass 1 kg tied to a light string of length l = 10 m is whirling in a circular path in the vertical
plane. If the ratio of the maximum to minimum tensions in the string is 3, find the speeds of the stone at
the lowest and highest points.​

Answer 1

The speed of the stone at  the lowest and highest points is 10 m/s.

Explanation:

Correct statement of the question

A stone of mass 1 kg  tied to a light inextensible string of length L= 10/3 m  is whirling in a  circular path of radius L in a vertical plane.  If the ratio of maximum to minimum tension in the string  is 4 and g= 10 m s to the power of minus 2 to the power of blank end exponent the speed of the stone at the highest point of the circle is?

Solution:

• The ratio of maximum to minimum tension is

T2/T1 = 4

T2 = 4T1

• Now the difference between two tensions should be 6 mg.

Thus we have

T2 - T1 = 6 mg

4T1 - T1 = 6 mg

3T1 = 6 mg

T1 = 2 mg

• Now the tensions at the top of the circle is

T1 + mg = mv1^2 / r = mv1^2 /L

2mg + mg = mv1^2 / 10/3

v1^2 = 3g x 10/3 = 10 g

v1 = √  10 x 10 = 10 m/s

Thus the speed of the stone at  the lowest and highest points is 10 m/s.

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