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Physics Question on rotational motion

An athlete throws a discus from rest to a final angular velocity of 15 rad s−115\, rad\, s ^{-1} in 0.270 s0.270\, s before releasing it. During acceleration, discus moves a circular arc of radius 0.810 m0.810 \,m. Acceleration of discus before it is released is

A

45 ms−245\,ms^{-2}

B

182 ms−2182\,ms^{-2}

C

187 ms−2187\,ms^{-2}

D

192 ms−2192\,ms^{-2}

Answer

45 ms−245\,ms^{-2}

Explanation

Solution

Given, angular velocity, ω=15 rad/s\omega=15\, rad / s
Time, t=0.270 st=0.270\, s
Radius, r=0.810 mr=0.810 \,m
Acceleration, a=vta=\frac{v}{t}
or a=rωta=\frac{r \omega}{t}
[∵v=rω][\because v=r \omega]
a=0.810×150.270a=\frac{0.810 \times 15}{0.270}
=45 m/s2=45 \,m / s ^{2}