A sphere of radius `10 cm` and mass `25` kg is attached to the lower end of a steel wire of length `5 m ` and diameter `4 mm ` which is suspended from the ceiling of a room . The point of support is `521 cm ` above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest position `(Y_(steel) = 2xx10^(11) N//m^(2))`.

Explanation

L = 5cm, l = 5.01 - 5 = 0.01 m, m = 25 kg
Young.s modulus `Y = (F//A)/(I //L) , A = pi xx (5 xx 10^(-4))^(2).^(2)`
`F = (YIA)/L =(20 xx 10^(10) xx 0.01 xx pi xx (5 xx 10^(-4))^(2))/5 = 314 N`
The tension in the string `T= mg + (mv^(2))/r,` where r = 5.11 m
The centripetal force `=(mv^(2))/r = T - mg = F-mg`
`v = sqrt((Fr)/m - gr) = sqrt((3.14 xx 5.11)/25) -9.8 xx 5.11) = 3.75` m/s