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

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

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

Squaring both sides of equation's i and ii and adding we get and using ,we get

The string tension b) is greater than mg

Centripetal Acceleration can be formulated as follows:

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Centripetal Force can be formulated as follows:

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:

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

Grade: High School

Subject: Physics

Chapter: Circular Motion

small = small current large mag large current

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000