Question

Locate the c.m. of a uniform cuboid of mass $m$ and having dimensions $(l \times b \times h)$.

   Locate the c.m. of a uniform cuboid of mass $m$ and having dimensions $(l \times b \times h)$.

Practice Problem in Physics for the JEE Main and Advanced

Practice Problem in Physics for the JEE Main and Advanced

Abhay Kumar 2015 Edition

Chapter 6, Problem 17

Instant Answer

Solved by Expert Hast Aggarwal

01/19/2022

Step 1

The mass density $\rho$ is given by the total mass $m$ divided by the volume of the cuboid. The volume of a cuboid is given by the product of its dimensions, so in this case, the volume is $l \times b \times h$. Therefore, the mass density is given by: \[\rho = Show more…

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Locate the c.m. of a uniform cuboid of mass $m$ and having dimensions $(l \times b \times h)$.

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Key Concepts

Cuboid Geometry

A cuboid is a three-dimensional rectangular object with six faces meeting at right angles. For such a shape with uniform density, symmetry dictates that the center of mass is located exactly at the midpoint of each of its dimensions, which is found by halving the lengths of the cuboid’s width, height, and depth.

Uniform Mass Distribution

A uniform mass distribution means that the density is constant throughout the volume of the object. Under this condition, the center of mass coincides with the geometric center because every segment of the body contributes equally to the mass distribution, simplifying calculations of the center of mass.

Center of Mass

The center of mass is the point in a body or system of bodies where the total mass of the system can be considered to be concentrated. It is the balance point of the object and plays a crucial role in analyzing the dynamics of motion, as it is the effective point where external forces act to cause translational movement.

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