Question

A particle of mass $0.2\, kg$ tied at the end of a spring is being rotated along a vertical circle of radius $0.5\, m$ at critical speed of $5 \,m/s$. The tension T in the string at the highest point of its path is

• A. 8.04 N
• B. 11.96 N
• C. 10 N
• D. 1.96 N

Answer 1

Answer: (A)

8.04 N

Answer 2

When a body tied to the end of a string is rotated in a vertical circle, the speed of the body is different at different points of the circular path when body is at highest point $A$, it is acted upon by two forces weight $m g$ of the body and tention $T_A$ in the string. $\therefore T_A + mg =$ centripetal force $= \frac{mv^2_A}{r}$ $\Rightarrow T_A = \frac{mv^2_A}{r} - mg$ Given, $m = 0.2\,kg, r = 0.5\,m, v_A = 5\,m/s$ $\therefore T_{A} =\frac{0.2 \times(5)^{2}}{0.5}-0.2 \times 9.8$ $T_{A} =10-1.96$ $T_{A} =8.04 \,N$