Home
Class 11
PHYSICS
The density of a non-uniform rod of leng...

The density of a non-uniform rod of length 1 m is given by `rho(x)=a(1+bx^(2))` where, a and b are constants and `0lexle1`. The centre of mass of the rod will be at ………..

A

`(3(2+b))/(4(3+b))`

B

`(4(2+b))/(3(3+b))`

C

`(3(3+b))/(4(2+b))`

D

`(4(3+b))/(3(2+b))`

Text Solution

Verified by Experts

The correct Answer is:
A
Density = `rho(x)=a(1+bx^(2))`
if `b=0`, then `rho(x)=a` = constant
Hence, centre of mass will be at middle of the rod, `x=0.5m`. Only (A) gives 0.5.
Promotional Banner

Topper's Solved these Questions

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    KUMAR PRAKASHAN|Exercise SECTION-D NCERT EXEMPLAR SOLUTIONS (VERY SHORT ANSWER TYPE QUESTIONS)|5 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    KUMAR PRAKASHAN|Exercise SECTION-D NCERT EXEMPLAR SOLUTIONS (SHORT ANSWER TYPE QUESTIONS)|4 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    KUMAR PRAKASHAN|Exercise SECTION-C OBJECTIVE QUESTIONS (VSQs)|52 Videos

  • QUESTIONS ASKED IN JEE - 2020

    KUMAR PRAKASHAN|Exercise Question|16 Videos

  • THERMAL PROPERTIES OF MATTER

    KUMAR PRAKASHAN|Exercise Question Paper (Section - D) (Answer following in brief :) Each carry 4 marks|1 Videos

Similar Questions

Explore conceptually related problems

The linear density of a non - uniform rod of length 2m is given by lamda(x)=a(1+bx^(2)) where a and b are constants and 0lt=xlt=2 . The centre of mass of the rod will be at. X=

The centre of mass of a non uniform rod of length L whoose mass per unit length varies as p=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

The coefficient of linear expansion 'alpha ' of the material of a rod of length l_(0) varies with absolute temperature as alpha = aT -bT^(2) where a & b are constant. The linear expansion of the rod when heated from T_(1) to T_(2) = 2T_(1) is :-

Obtain the position of centre of mass of a thin rod of uniform density.

A rod of length L and cross section area A has variable density according to the relation rho (x)=rho_(0)+kx for 0 le x le L/2 and rho(x)=2x^(2) for L/2 le x le L where rho_(0) and k are constants. Find the mass of the rod.

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O

The area of cross-section of rod is given by A= A_(0) (1+alphax) where A_(0) & alpha are constant and x is the distance from one end. If the thermal conductivity of the material is K . What is the thermal resistancy of the rod if its length is l_(0) ?

A solid non conducting sphere of radius R has a non-uniform charge distribution of volume charge density, rho=rho_(0)r/R , where rho_(0) is a constant and r is the distance from the centre of the sphere. Show that : (i) the total charge on the sphere is Q=pirho_(0)R^(3) (ii) the electric field inside the sphere has a magnitude given by, E=(KQr^(2))/R^(4)

The moment of inertia of a rod about an axis through its centre and perpendicular to it is (1)/(12)ML^(2) (where M is the mass and L, the length of the rod). The rod is bent in the middle so that the two halves make an angle 60^(@) . The moment of inertia of the bent rod about the same axis would be..........