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
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$
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.
