In the 1st figure shown here rod is massless and at its end a bob of mass m is attached. The other figure is a uniform rod also of mass m. As they are released, at the bottom


A. The bob has higher kinetic energy but lower angular velocity
B. The bob has higher kinetic energy as well higher angular velocity
C. The bob has lower kinetic energy but higher angular velocity
D. The bob has lower kinetic energy as well lower angular velocity

Options

A. The bob has higher kinetic energy but lower angular velocity
B. The bob has higher kinetic energy as well higher angular velocity
C. The bob has lower kinetic energy but higher angular velocity
D. The bob has lower kinetic energy as well lower angular velocity

Explanation

(i) `tau_("net")=PE sin 53^(@)= I alpha`
`:. alpha=((ql) E (4/5))/((ml^(2))/12+m(l/2)^(2)+m(l/2)^(2))=(48qE)/(35 ml)`
(ii) From energy conservation : `K_(i)+U_(i)=K_(f)+U_(f)`
`:. 0+(-PE cos 53^(@))=1/2 Iomega^(2)+(-PE cos 0^(@))`
where `I=(ml^(2))/12+m (l/2)^(2)+m(l/2)^(2)=(7ml^(2))/12" ":." "1/2 Iomega^(2)=PE (1-3//5)=2/5 PE`
`:. 1/2xx(7 m l^(2))/12xxomega^(2) =2/5" "qlE` or `omega=sqrt((48 qE)/(35 ml))`
(iii) `:' W_("ext")=U_(f)-U_(i)`
`:. W_("ext")=(-PE cos (180^(@)+53^(@)))-(-PE cos 53^(@))`
or `W_("ext")=(ql)E(3/5)+(ql)E(3/5)" "implies" "W_("ext")=(6/5) qlE`