Question

When a ball at rest hangs by a single vertical string, tension in the string is mg. If the ball is made to move in a horizontal circle so that the string describes a cone, string tension
a) is mg. b) is greater than mg, always. c) is less than mg, always. d) may be greater or less than mg depending on the speed of the ball

Answer 1

Answer:

The correct answer is option 'b': is greater than mg always.

Explanation:

The situation is represented in the attached figure

In the figure we can see that

For equlibrium in y direction we have

$Tcos(\theta )=mg........(i)$

For the motion of the in the horizantal circle we can write

$Tsin(\theta )=\frac{mv^{2}}{r}..........(ii)$

Squaring both sides of equation's i and ii and adding we get and using $cos^{2}(\theta )+sin^{2}(\theta )=1$,we get

$T^{2}cos^{2}(\theta )+T^{2}sin^{2}(\theta )=m^{2}g^{2}+\frac{m^{2}v^{4}}{r^{2}}\\\\T^{2}=(mg)^{2}(1+\frac{v^{4}}{(rg)^{2}})\\\\\therefore T=mg\times (1+\frac{v^{4}}{(rg)^{2}})^{1/2}\\\\\therefore T> mg$$\because ((1+\frac{v^{4}}{(rg)^{2}})^{1/2})>1)$

Answer 2

The string tension b) is greater than mg

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Further explanation

Centripetal Acceleration can be formulated as follows:

$\large {\boxed {a = \frac{ v^2 } { R } }$

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

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Centripetal Force can be formulated as follows:

$\large {\boxed {F = m \frac{ v^2 } { R } }$

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

Given:

weight of ball = mg

Asked:

string tension = T = ?

Solution:

$\Sigma Fy = 0$

$Ty - mg = 0$

$Ty = mg$

$T\cos \theta = mg$

$\boxed{T = mg \div \cos \theta}$

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As we know that the maximum value of cos θ = 1 , then :

$\cos \theta < 1$

$mg \div T < 1$

$mg < T$

$\boxed{T > mg}$

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Learn more

• Impacts of Gravity : https://brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
• The Acceleration Due To Gravity : https://brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion