A particle at rest starts moving with constant angular accelerati… - Vidyadip

MCQ

A particle at rest starts moving with constant angular acceleration $4

rad / s ^2$ in circular path.At what time the magnitude of its tangential acceleration and centrifugal acceleration will be equal?

A
$0.4 s$
✓
$0.5 s$
C
$0.8 s$
D
$1.0 s$

✓

Answer

Correct option: B.

$0.5 s$

(b) : Here : angular acceleration, $\alpha=4 rad / s ^2$
$
\frac{d \omega}{d t}=4 \Rightarrow \omega=4 t rad / s ; v=r \omega=4 t r
$
Given, $a_T=a_C \Rightarrow \alpha r=\frac{v^2}{r} \Rightarrow 4 r=\frac{16 t^2 r^2}{r}$
$
\Rightarrow t^2=\frac{1}{4} \Rightarrow t=0.5 sec
$

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