Home
Class 11
PHYSICS
Half of the recrtangular plate shown in ...

Half of the recrtangular plate shown in figure is made of a material of density `rho_1` and the other half of density `rho_2`. The length of the plate is L. Locate the centre of mass of the plate.

Text Solution

Verified by Experts

The centre of mass of each half is located at the geometricla centre of that half. Thus the left half may be replced by a pont particle of mss `Krho_1` placed at C_1` and the right half may be replaced by a point particle of mass `Krho_2` placed at `C_2`. This replacement is for the specific purpose of locatig the combined centre of mass. Take the middle point of the left edge to be the origin. The x-cordiN/Ate of the centre of mass is
`x=((Krho_1)L/4+(Krho_2)(3L)/3)/(Krho_1+Krho_2)`
`=(rho_1=3rho_2)/(4(rho_1+rho_2)) L`
the combined centre of mass is this much to the right of the assumed origin.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CENTRE OF MASS, LINEAR MOMENTUM, COLLISION

    HC VERMA|Exercise Question For short Answer|25 Videos

  • CENTRE OF MASS, LINEAR MOMENTUM, COLLISION

    HC VERMA|Exercise Objective -1|18 Videos

  • CENTRE OF MASS, LINEAR MOMENTUM, COLLISION

    HC VERMA|Exercise Exercises|64 Videos

  • CALORIMETRY

    HC VERMA|Exercise Exercises|18 Videos

  • CIRCULAR MOTION

    HC VERMA|Exercise Exercises|30 Videos

Similar Questions

Explore conceptually related problems

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

A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of san edge of the plate . Locate the centre of mass of the combination assuming same mass per unit area for the two plates.

Knowledge Check

  • A circular plate of diameter 10 cm is kept in contact with a square plate of side 10 cm. The density of the material and the thickness are same everywhere. The center of mass of the system will be

    A
    inside the circular plate
    B
    inside the square plate
    C
    At the point of contact
    D
    outside the system

    • Similar Questions

    Explore conceptually related problems

    A uniform electric field E is created between two parallel ., charged plates as shown in figure . An electron . enters the field symmetrically between the plataes with a . speed v_0. The length of each plate is l. Find the angle of . deviation of the path of the electron as it comes out . of the field.

    Each of the three plates shown in figure has an area of 200 cm^2 on one side and the gap between the adjacent plates is 0.2 mm. The emf of the battery is 20V. Find the distribution of charge on various surfaces of the plates. What is the equivalent capacitance of the system between the terminal points?

    A circular plate of diameter d is kept in contact with a square plate of edge d as shown in figure. The densit of the material and the thickness are same . Everywhere. The centre of mass of the composite system will be

    Seven homogeneous bricks, each of length L are arranged as shown in figure. Each brick is displaced with respect to the one in contact by L/10 . Find the x-coordinate of the centre of mass relative to the origin shown.

    Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density sigma as shown in figure (30-E6). Find the electric field (a) at the left of the plates, (b) in between the plates and © at the right of the plates.

    A particle of mass m and charge (-q) enters the region between the two charged plates initrally moving along X-axis with speed V_(x) as shown in figure. The length of plate is L and an uniform electric field E is maintained between the plates. S.T. vertical deflection of the particle at the edge of the plate is (qEL^(2))/(2mV_(x)^(2)) .

    A plate of thickness t made of a material of refractive index mu is placed in front of one of the slits in a double slit experiment. (a) Find the changes in he optical path due to introduction of the plate. (b) Wht should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero ? Wavelength of the light used is lamda . Neglect any absorption of light in the plate.

    Home
    Profile