Question

A point starts from rest and moves along a circular path of radius $20cm$ with a constant tangential acceleration of $5cm/s^2$. The time needed for the centripal acceleration of the point to be equal to its tangential acceleration is:

• A. $0.2s$
• B. $0.5s$
• C. $1s$
• D. $2s$

Answer 1

The correct option is D $2s$

Let at time $t$,

Centripetal acceleration= Tangential acceleration

$\Rightarrow \frac{v^2}{R}=a_t$ $\Rightarrow v=\sqrt{a_{t}R}=\sqrt{5\times 20}=10cm/s$

Using $v=u+at$, $\Rightarrow t=\frac{v}{a}=\frac{10}{5}=2s$