Grade 12th passIIT JEE Entrance Exam

A particle is attached to one end of string the other end of which is fixed. The particle moves in vertical plane. The velocity at the lowest point is such that the particle can just complete the circle. The ratio of tension in string at A&B is

Abhinav Jain

6 Years agoGrade 12th pass

2 Answers

Md Mushahid

6 Years ago

when an object of mass m which is fixed to an end of an inextensible and light rod

and revolving around a circular path about the other end,

weight of the object and tension in the rod are getting adjusted to provide centripetal force as shown in figure,

Let us consider when the object is at B, as shown in figure.

Centripetal force $\frac{m\times v^{2}}{I} =T - mg\cos \theta$

where T is tension in the rod, m is mass of object and θ is the angular dispalcement

when the vertical position is taken as reference.

When the object is at A, θ = 0. hence centripetal force $\frac{m\times v^{2}}{I} =T - mg$ -------------2

When the object is at the top most position C, θ = π, hence centripetal force $\frac{m\times v^{2}}{I} =T + mg$ ............(3)

When the object is at top most position C, minimum required velocity vmin is obtained,

by considering tension in the rod T is zero.

when we apply this condition in eqn.(3), we get vmin = $\sqrt{gl}$

Vikas TU

6 Years ago

The Expression for Velocity of Body Moving in a Vertical Circle: Consider a small body of mass 'm' attached to one end of a string and whirled in a vertical circle of radius 'r'. In this case, the acceleration of the body increases as it goes down the vertical circle and decreases when goes up the vertical circle.
The ratio of tension would be = 2mg/8mg = 0.25