Question

The acceleration of a body in a non-uniform circular motion is $5{ms}^{-2}$. Which one of the following is correct ?

• A. The radial acceleration and the tangential accelerations are $3{ms}^{-2}$ and $4{ms}^{-2}$ respectively.
• B. The radial and the tangential accelerations are $2{ms}^{-2}$ and $3{ms}^{-2}$ respectively.
• C. The radial and the tangential accelerations are both $5{ms}^{-2}$
• D. The radial and the tangential acceleration are $5{ms}^{-2}$ and $3{ms}^{-2}$ respectively.

Answer 1

The correct option is A The radial acceleration and the tangential accelerations are $3{ms}^{-2}$ and $4{ms}^{-2}$ respectively.

Acceleration of the body $a=5m/s^2$

Let the radial and tangential acceleration be $a_c$ and $a_t$ respectively.

$\therefore$ $a=\sqrt{a_t^2+a_c^2}$

For option A : $a_c=3m/s^2$ and $a_t=4m/s^2$

$\therefore$ $a=\sqrt{4^2+3^2}=\sqrt{25}=5m/s^2$

Thus option A is correct.