Question

A particle moving along a circular path of radius $6m$ uniform speed of $8m{s}^{-1}$ . The average acceleration when the particle completes one half of the revolution is -

• A. $\frac{16}{3\pi }m/s^2$
• B. $\frac{32}{3\pi }m/s^2$
• C. $\frac{64}{3\pi }m/s^2$
• D. None of these

Answer 1

The correct option is C $\frac{64}{3\pi }m/s^2$

A particle moving along a circular path of radius 6m uniform speed of $8m{s}^{-1}.$

the particle has velocity tangential to the circle all the time when particle complete half the circle than its change its direction opposite to each other.

initial and final velocity is $v_1$ and $v_2$

$v_1=-8\hat{i},v_2=8\hat{i}$

time taken $t=\frac{s}{v}=\frac{\pi R}{8}=\frac{6\pi }{8}$

acceleration=(change in velocity)/(total time taken)

$a=\frac{v_2-v_1}{t}=\frac{8-(-8)}{\frac{6\pi }{8}}=\frac{64}{3\pi }$

Hence the correct answer is C