Question

A stone is moved in a horizontal circle of radius 4m by means of a string at a height of 20m above the ground. The string breaks and the particle' flies off horizontally, striking the ground 10m away. The centripetal acceleration during circular motion is

• A. $6.25{ms}^{-2}$
• B. $12.5{ms}^{-2}$
• C. $18.75{ms}^{-2}$
• D. $25{ms}^{-2}$

Answer 1

Answer: (A)

$6.25{ms}^{-2}$

The stone falls by height $20m$. Hence the time of flight can be found out by $h=\frac{1}{2}a{t}^2$

$⟹t=\sqrt{\frac{2h}{a}}$ $=\sqrt{\frac{2\times 20}{10}}s$ $=2s$

The range of the flight $=vt=R$

$⟹v=\frac{10m}{2s}=5m/s$

Hence the centripetal acceleration $=\frac{v^2}{r}$ $=\frac{25m^2/s^2}{4m}=6.25m/s^2$