Home
Class 11
PHYSICS
Find out the location of centre of mass ...

Find out the location of centre of mass of a uniform rod.

Text Solution

Verified by Experts

Suppose a rod of mass M and length L is lying along the x-axis with its one end at x=0 and the other at x = L
Mass per unit length of the rod =`M/L`
Hence, mass of the element PQ of length dx situated at a distance V from the origin is dm =`M/L` dx
The coordinates of the element PQ are (x, 0,0). Therefore, x -coordinate of CM of the rod will be:
`x_(CM) = (int_(0)^(L)xdm)/(intdm) =(int_(0)^(L)(x)(M/Ldx))/M = I/L int_(0)^(L) xdx = L/2, y_(cm) =(int ydm)/(int dm)=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

What is the location of the centre of mass of a uniform triangular lamina ?

Find the position of centre of mass of the uniform lamina shown in figure.

Find the centre of mass of a uniform solid cone.

Two identical uniform rods AB and CD, each of length L are jointed to form a T-shaped frame as shown in figure. Locate the centre of mass of the frame. The centre of mass of a uniform rod is at the middle point of the rod.

The linear mass density lambda of a rod AB is given by lambda =alpha+betax kg/m taking O as origin. Find the location of the centre of mass from the end A?

Given the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie on the body ?

Mass center of a system of a segment of a uniform circular rod(arc) Find location of mass center of a thin uniform rod bent into shape of an arc.

A uniform thin rod of mass m and length l is standing on a smooth horizontal suface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Find the velocity of centre of mass of the rod at the instant when it makes an angle theta with horizontal.

Mass Center of a sector of a uniform circular plate Find location of mass center of a sector of a thin uniform plate.

Find the centre of mass of a uniform semicircular ring of radius R and mass M .