Question

The magnitude of the tangential acceleration of a particle moving in a circle of radius $10cm$ with uniform speed completing the circle in a $4s$.

• A. $2.5{\pi }^2$ $cm/s^2$
• B. $1.5{\pi }^2$ $cm/s^2$
• C. $2{\pi }^2$ $cm/s^2$
• D. $3{\pi }^2$ $cm/s^2$

Answer 1

The correct option is A $2.5{\pi }^2$ $cm/s^2$

the distance covered in completing the circle is =$2\pi r=2\ast 10\pi =20\pi cm$

Linear speed =$\frac{2\pi r}{t}=\frac{20\pi }{4}=5\pi cm/sec$

Linear acceration = $a=\frac{v^2}{r}=\frac{(5\pi cm/sec{)}^2}{10cm}=2.5{\pi }^{2}cm/se{c}^2$