Question

An object moves at a constant speed along a circular path in a horizontal $X-Y$ plane, with the centre at the origin. When the object is at $x=-2 \,m$ , its velocity is $-4 \hat{j} m s ^{-1}$ What is the object's acceleration when it is $y=2 \,m$ ?

• A. $-8 \hat{j} \,m \,s ^{-2}$
• B. $-8 \hat{i} \,m \,s ^{-2}$
• C. $-4 \hat{j} \,m \,s ^{-2}$
• D. $4 \hat{i} \,m \,s ^{-2}$

Answer 1

Answer: (A)

Here, radius of circular path, $r=2\, m$
Speed of the object, $v=4\, m \,s ^{-1}$

The magnitude of centripetal acceleration
$a_{c}=\frac{v^{2}}{r}=\frac{4^{2}}{2}=8 m s ^{-2}$
This acceleration is directed towards the centre.
Therefore, when the object is at $y=2 m ,$
its position is $P$ (see figure).
Its acceleration is $-8 \hat{j} \,m \,s ^{-2}$.