a particle of mass(m) attack to a string of length (r) b wave round in a circle with speep(b) fine the form of the expression for the tension the string
m*V^2/r is the tension
I suspect you meant the speed is V, not the speep is b.
To find the expression for the tension in the string, we can start by considering the forces acting on the particle as it moves in a circular path.
1. Centripetal Force: The tension in the string provides the centripetal force required to keep the particle moving in a circle. This force acts towards the center of the circle.
2. Gravitational Force: The particle also experiences the gravitational force acting downward.
Let's break down the steps to derive the expression for the tension:
Step 1: Centripetal Force
The centripetal force (F_c) is given by the equation:
F_c = m * a_c
where m is the mass of the particle and a_c is the centripetal acceleration.
The centripetal acceleration is defined as:
a_c = v^2 / r
where v is the speed of the particle and r is the radius of the circular path (string length).
Substituting the value of a_c in the equation for F_c:
F_c = m * (v^2 / r)
Step 2: Gravitational Force
The gravitational force (F_g) acting on the particle is given by:
F_g = m * g
where g is the acceleration due to gravity.
Step 3: Equating the Forces
Since there are no other forces acting on the particle in the circular motion, we can equate the centripetal force and gravitational force:
F_c = F_g
m * (v^2 / r) = m * g
Step 4: Solving for the Tension
Both m and g are common to both sides of the equation, so they can be canceled out:
(v^2 / r) = g
Now we can isolate v^2:
v^2 = g * r
Finally, we substitute this value of v^2 in the equation for centripetal force:
F_c = m * (g * r / r)
Simplifying:
F_c = m * g
Therefore, the expression for the tension in the string is T = m * g, where T represents the tension, m represents the mass of the particle, and g represents the acceleration due to gravity.