An air puck of mass `m_(1)` is tied to a string allowed to revolved in a circle of radius `R` on a frictionless horizontal table . The other end of the string passes through a small hole in the centre of the table , and a load of mass `m_(2)` is tied to the string? The suspended load remains in equilibrium while the pack on the tabletop revolves.

a. Find the tension in the string
b. Find the radial force acting on the puck
c. Find the speed of the puck
d. Qualitaively describe what will happen in the motion of the puck if the value of `m_(2)` is somewhat increased by placing an additional load on it.
e.Qualitaively describe what will happen in the motion of the puck if the value of `m_(2)` is instead decreased removing a part from the hanging load.

Explanation

a. since the object of mass `m_(2)` is in equilibrium.
` sum F_(y) = T - mg = 0 or T = m_(2) g`
b.The tension in the string provides the required contripetal acceleration of the pack
Thus `F_(c) = T = m_(2)g`
c. From `F_(c) = (m_(1)v^(2))/(R)` , we have `v = sqrt((RF_(c))/(m_(1))) = sqrt(((m_(2))/(m_(1)))) gR`
d.The pack will spiral inward, gaining speed as it does as It gain speed because the extra large string tension produces forward tengntial acceleration as well as inward redial acceleration of the pack , pulling at an angle of less than `90^(@)` to the direction of the inward spiraling velocity
e. The pack will spiral outward slowing down as it does so