Home
Class 12
PHYSICS
A uniform thin rod AB of length L has li...

A uniform thin rod AB of length L has linear mass density `mu(x) = a + (bx)/(L)`, where x is measured from A. If the CM of the rod lies at a distance of `((7)/(12)L)` from A, then a and b are related as :_

A

`2a = b `

B

`a = 2b `

C

`a = b `

D

`3a = 2b`

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • NTA JEE MOCK TEST 96

    NTA MOCK TESTS|Exercise PHYSICS|25 Videos

  • NTA JEE MOCK TEST 98

    NTA MOCK TESTS|Exercise PHYSICS|24 Videos

Similar Questions

Explore conceptually related problems

A thin rod AB of length a has variable mass per unit length rho_(0) (1 + (x)/(a)) where x is the distance measured from A and rho_(0) is a constant. Find the mass M of the rod.

The linear mass density of a thin rod AB of length L varies from A to B as lambda (x) =lambda_0 (1 + x/L) . Where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicualr to the rod is :

Knowledge Check

  • Find centre of mass of given rod of linear mass density lambda=(a+b(x/l)^2) , x is distance from one of its end. Length of the rod is l .

    A
    `(3l)/4((3a+b)/(2a+b))`
    B
    `(3l)/4((2a+b)/(3a+b))`
    C
    `(l)/4((2a+b)/(3a+b))`
    D
    `l((2a+b)/(3a+b))`

  • A rod length L and mass M is placed along the x -axis with one end at the origin, as shown in the figure above. The rod has linear mass density lamda=(2M)/(L^(2))x, where x is the distance from the origin. Which of the following gives the x -coordinate of the rod's center of mass?

    A
    `2/3L`
    B
    `1/4L`
    C
    `1/3L`
    D
    `1/2L`

  • The mass per unit length of a non - uniform rod of length L is given mu = lambda x^(2) , where lambda is a constant and x is distance from one end of the rod. The distance of the center of mas of rod from this end is

    A
    `(L)/(2)`
    B
    `(L)/(4)`
    C
    `(3L)/(4)`
    D
    `(L)/(3)`

    • Similar Questions

    Explore conceptually related problems

    A thin rod AB of length a has variable mass per unit length P_(0) (1 + (x)/(a)) where x is the distance measured from A and rho_(0) is a constant. Find the position of centre of mass of the rod.

    The mass per unit length of a non- uniform rod OP of length L varies as m=k(x)/(L) where k is a constant and x is the distance of any point on the rod from end 0 .The distance of the centre of mass of the rod from end 0 is

    You are given a rod of length L. The linear mass density is lambda such that lambda=a+bx . Here a and b are constants and the mass of the rod increases as x decreases. Find the mass of the rod

    The mass per unit length of a non-uniform rod of length L is given by mu= lamdaxx2 ​, where lamda is a constant and x is distance from one end of the rod. The distance of the center of mass of rod from this end is :-

    The centre of mass of a non uniform rod of length L whoose mass per unit length varies asp=kx^(2)//L , (where k is a constant and x is the distance measured form one end) is at the following distances from the same end

    Home
    Profile