Question:
Three bricks each of length $L$ and mass $M$ are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
Three bricks each of length $L$ and mass $M$ are arranged as shown from the wall. The distance of the centre of mass of the system from the wall is
Updated On: Jan 10, 2024
- $ L/4 $
- $ L/2 $
- $ (3/2)L $
- $ (11/12)L $
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The Correct Option is D
Solution and Explanation
$ {{x}_{1}}=\frac{L}{2} $
$ {{x}_{2}}=L $
$ {{x}_{3}}=L+\frac{L}{4} $
$ {{x}_{3}}=\frac{5L}{4} $
$ \therefore $ $ {{x}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{2}}{{x}_{3}}}{3m} $
$ =\frac{\frac{mL}{2}+mL+\frac{m5L}{4}}{3m} $
$ =\frac{11L}{12} $
$ {{x}_{2}}=L $
$ {{x}_{3}}=L+\frac{L}{4} $
$ {{x}_{3}}=\frac{5L}{4} $
$ \therefore $ $ {{x}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{2}}{{x}_{3}}}{3m} $
$ =\frac{\frac{mL}{2}+mL+\frac{m5L}{4}}{3m} $
$ =\frac{11L}{12} $
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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.