Home
Class 11
PHYSICS
If linear density of a rod of length 3m ...

If linear density of a rod of length 3m varies as `lamda=2+x`, then the position of the centre of mass of the rod is `P/7m`. Find the value of P.

A

`(7)/(3)m`

B

`(12)/(7)m`

C

`(10)/(7) m`

D

`(9)/(7) m`

Text Solution

Verified by Experts

The correct Answer is:
B
`lamda = (2+x) , l=3m`
`x_(CM)= (int x dm)/(int dm)= (underset(0)overset(3)int x (2+x) dx)/(underset(0)^(3)int (2+ x) dx)`
`= (underset(0)overset(3)int (2x+ x^(2)) dx)/(underset(0)^(3)int (2+x) dx)= ([x^(2) + (x^(3))/(3)]_(0)^(3))/([2x+ (x^(2))/(2)]_(0)^(3))`
`= (9+ (27)/(3))/(6+ (9)/(2))= (18)/(21) xx 2= (12)/(7)m`
Promotional Banner

Similar Questions

Explore conceptually related problems

If linear density of a rod of length 3m varies as lambda = 2 + x, them the position of the centre of gravity of the rod is

If the linear density of a rod of length L varies as lambda = A+Bx , find the position of its centre of mass .

If the linear mass density of a rod of length 3 m (lying from y=0 to y=3 m) varies as lambda =(2+y)kg/m,then position of the centre of mass of the rod from y=0 is nearly at

The linear density of a thin rod of length 1m lies as lambda = (1+2x) , where x is the distance from its one end. Find the distance of its center of mass from this end.

Mass is non-uniformly distributed over the rod of length l, its linear mass density varies linearly with length as lamda=kx^(2) . The position of centre of mass (from lighter end) is given by-

The density of a linear rod of length L varies as rho=A+Bx where x is the distance from theleft end. Locate the centre of mass.

If linear mass density a rod of length 2 m is changing with position as [lambda =(3x + 2)] kg m then mass of the rod with one end at origin will be

Find the MI of a rod about an axis through its centre of mass and perpendicular to the length whose linear density varies as lamda = ax where a is a constant and x is the position of an element of the rod relative to it's left end. The length of the rod l .

The density of a thin rod of length l varies with the distance x from one end as rho=rho_0(x^2)/(l^2) . Find the position of centre of mass of rod.

A rod of mass m and length L is non- uniform.The mass of rod per unit length (mu)], varies as "(mu)=bx" ,where b is a constant.The , centre of mass of the ,rod is given by