Question

A particle is moving along a curve. Then, choose the correct option(s).

• A. If its speed is constant, it has no acceleration.
• B. If its speed is increasing, the acceleration of the particle is along its direction of motion.
• C. If its speed is constant, the magnitude of its acceleration is inversely proportional to its radius of curvature.
• D. The direction of its acceleration cannot be along the tangent.

Answer 1

Answer: (C), (D)

The direction of its acceleration cannot be along the tangent.

Option (A) is incorrect, because due to a change in direction of velocity, there will be a nonzero acceleration even when the speed is constant.

Option (B) is also incorrect because if speed is increasing, then there will be both tangential acceleration and centripetal acceleration. Therefore the acceleration will not be along the direction of its motion. It will be in the direction of the total acceleration which is the vector sum of centripetal and tangential acceleration.

In a curved path with constant speed, the acceleration is the centripetal acceleration. The value of centripetal acceleration is given by the equation
$a_{cen}=\frac{v^2}{r}$
where $v=$ linear velocity & $r=$ radius of curvature of the path.

Thus, option (C) is correct.

Since centripetal acceleration will always exist for motion along a curve, the direction of total acceleration cannot be along the tangent for any motion. Hence, option (D) is also correct.

Therefore, option (C) & (D) are correct.