Question

A small bob of mass m is tied to a string and revolved in a vertical circle of radius r. If its speed at the highest point is √3rg, the tension in the string at the lowest point is 

(A) 5 mg 

(B) 6 mg 

(C) 7 mg 

(D) 8 mg.

Answer 1

Correct Option is (C) 7 mg

\(E_i = E_f\)

\(\frac{1}{2} mv_o{^2}\) = \(\frac{1}{2} mv{^2} + mgh\)

\(\frac{1}{2} mv_o{^2}\) = \(\frac{1}{2} \times m \times (\sqrt{3rg})^2 + mgh\)

\(\frac{1}{2} mv_o{^2}\) = \(\frac{3}{2} mrg + mg(2r)\)

\(\frac{1}{2} mv_o{^2}\) = \(\frac{3}{2} mrg + 2mgr\)

\(\frac{1}{2} mv_o{^2}\) = \(\frac{3mrg \ + \ 4 mrg}{2}\)

\(mv_o{^2}\) = \(7mrg\)

\(v_o = \sqrt{7rg}\)

\(T = \frac{mv^2}{r}\)

\(= \frac{m}{r}(\sqrt{7rg})^2\)

\(T = 7mg\)

Answer 2

Correct option is (C) 7 mg.