Question

A heavy particle is suspended by a string of length $60\, cm$ from a fixed point $O$. It is projected horizontally with speed $4.2\, m / s$ from its lowest position: (Take $g=9.8\, m / s ^{2}$ )

• A. The particle will rise to a maximum height of $30\, cm$ above $O$.
• B. The maximum height above $O$ reached by the particle will be less than $30 \, cm$.
• C. When the particle reaches the maximum height it will have kinetic energy.
• D. The particle will leave the circular path while going up.

Answer 1

Answer: (B), (C), (D)

The minimum speed requierd to complete the circular motion is $(5 g l)^{1 / 2}=5.42 \,m / s$ which is more than the imparted speed so particle will not be able to attain the maximum height due to the initial speed which is $v^{2} / 2 g=90\, m$. The string will slack before it reaches thê 90 height abovee thê initial point.