Home
Class 11
PHYSICS
Consider a rectangular plate of dimensio...

Consider a rectangular plate of dimensions `axxb`. If this plate is considered to be made up of four rectangles of dimensions `a/2xxb/2` and we now remove one out of four rectangles. Find the position where the centre of mass of the remaining system will lie?

Text Solution

Verified by Experts

The correct Answer is:
A, B
`x_(CM)=(A_1x_1-A_2x_2)/(A_1-A_2)`
`=((ab)(0)-((ab)/(4))(a/4))/(ab-(ab)/(4))`
`=-a/12`
`y_(CM)=(A_1y_1-A_2y_2)/(A_1-A_2)`
`=((ab)(0)-((ab)/(4))(b/4))/(ab-(ab)/(4))`
`=-b/12`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

    DC PANDEY|Exercise Level 1 Subjective Questions|1 Videos

  • CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

    DC PANDEY|Exercise Level 2 Single Correct|23 Videos

  • CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

    DC PANDEY|Exercise Level 1 Objective|42 Videos

  • CENTRE OF MASS, IMPULSE AND MOMENTUM

    DC PANDEY|Exercise Comprehension type questions|15 Videos

  • CIRCULAR MOTION

    DC PANDEY|Exercise Medical entrances s gallery|19 Videos

Similar Questions

Explore conceptually related problems

A circular plate of uniform thickness has a diameter fo 56cm. A circular portion of diameter 42 cm is removed from one edge of the plate as shown in figure. Find the position of the centre of mass of the remaining portion.

A square of side 4 cm and of uniform thickness is divided into four equal squares. If one of them is cut off (OECF), then the position of the centre of mass of the remaining portion from O is (sqrt2)/k cm . Find the value of K.

Knowledge Check

  • There is a rectangular metal plate in which two cavities in the shape of rectangle and circle are made, as shown with dimensions. P and Q are the centres of these cavities. On heating the plate, which of the following quantities increases?

    A
    `pir^(2)`
    B
    `ab`
    C
    `R`
    D
    `b`

    • Similar Questions

    Explore conceptually related problems

    A rectangular plate of dimensions l xx b is in x -y plane as shown in Fig. If the portion of this plate lying in quadrant I is removed, find the position of centre of mass of remaining part of plate.

    Rectangle MNOP is made up of four congruent rectangles (Fig. 9.31). If the length of one of the rectangle is 8 m and breadth is 2 m, then find the perimeter of MNOP.

    Four particles of mass m are connected by massless rods to form a rectangle-of sides 2a and 2b as shown. The assembly, rotates about an axis in the plane of the figure through the centre. Find the moment of inertia about the axis:,

    The centre of mass of three particles of masses 1 kg, 2kg and 3 kg lies at the point (3m, 3m, 3m) where should a fourth particles of mass 4 kg be positioned so that centre of mass of the four particle system at (1m, 1m, 1m) ?

    The centre of mass of three particles of masses 1kg, 2 kg and 3kg lies at the point (3m, 3m, 3m). Where should a fourth particle of mass 4 kg be positioned so that the centre of mass of the four particle system lies at the point (1m, 1m, 1m)?

    The coordinates of the centre of mass of a system of three particles of mass 1g,2g and 3g are (2,2,2). Where should a fourth particle of mass 4 g be positioned so that the centre of mass of the four particle system is at the origin of the three-dimensional coordinate system ?

    Four point particles of masses 1.0 kg, 1.5 kg, 3.0 kg and 2.5 kg are placed at four corners of a rectangle of sides 4.0 cm and 3.0 cm as shown in the figure. The centre of mass of the system is at a point:

    Home
    Profile