Asphere of radius 10 cm and mass 25 kg isattached to the lower end of a steel wire of length 5 mand diameter 4 mmwhich is suspended from the ceiling of a room . The pointof support is 521 cmabove 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)).

Asphere of radius 10 cm and mass 25 kg isattached to the lower end of

1.	Asphere of radius 10 cm and mass 25 kg isattached to the lower end of a steel wire of length 5 mand diameter 4 mmwhich is suspended from the ceiling of a room . The pointof support is 521 cmabove 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)).
Answer» SOLUTION :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