Question

a mass of 0.4 kg is rotated at a constant speed v in a vertical circle of radius one metre is the minimum tension in the string is 3 Newton calculate v the maximum tension the tension when the string is just horizontal
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Answer 1

Answer:

Tmax= 10.98N and v=4.18m/s

Explanation:

Given,

Tension is max at lowest point

Tension is min at highest point.

Tmin = mv2/r-mg

or, 3=0.4*v2/1-0.4*10

or, (3+4)/0.4=v2

or, v=4.18m/s

tmax= mv2/r+mg

=10.98N Ans

Answer 2

Given:

Mass of a body(m)= 0.4 kg

Speed= v(let)

Radius of circle(r)= 1 m

Minimum tension in the string(Tmin)= 3 N

Maximum tension in the string(Tmax) =?

Acceleration due to gravity(g)= 9.8 m/s²

To calculate the speed of moving object and maximum tension produced in the string

Solution:

When the object rotates vertically in a circle, the minimum tension (Tmin) produced in the string will be,

$Tmin=mv^{2} /r -mg$

⇒3=0.4×v²/1 - 0.4×9.8

⇒6.92=0.4v²

⇒v²=6.92/0.4

∴v= 4.16 m/s

Again,

Maximum tension will be produced when the string is just horizontal. Thus, Tmax is given as,

$Tmax=mv^{2} /r +mg$

          =0.4×(4.16)²/1 + 0.14×9.8

∴Tmax =8.29 N

Hence, the value of v is 4.16 m/s, and the maximum tension when the string is just horizontal is 8.29 N.

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