Question:
Four particles, each of mass 1 kg are placed at the comers of a square OABC of side 1 m. O is at the origin of the co-ordinate system. OA and OC are aligned along positive X-axis and positive V-axis respectively. The position vector of the centre of mass is (in m):
Four particles, each of mass 1 kg are placed at the comers of a square OABC of side 1 m. O is at the origin of the co-ordinate system. OA and OC are aligned along positive X-axis and positive V-axis respectively. The position vector of the centre of mass is (in m):
Updated On: May 9, 2024
- $ \widehat{i}-\widehat{j} $
- $ \frac{1}{2}(\widehat{i}+\widehat{j}) $
- $ (\widehat{i}-\widehat{j}) $
- $ \frac{1}{2}(\widehat{i}-\widehat{j}) $
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The Correct Option is B
Solution and Explanation
We can show the situation as : The centre of mass of square is at point $ D(x,y) $ The position co-ordinate of point D $ (x,y)\equiv \left( \frac{0+1}{2},\frac{1+0}{2} \right) $ $ =\left( \frac{1}{2},\frac{1}{2} \right) $ Hence, position vector or centre of mass D is $ =x\hat{i}+y\hat{j} $ $ =\frac{1}{2}\hat{i}+\frac{1}{2}\hat{j} $ $ =\frac{1}{2}(\hat{i}+\hat{j}) $
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.