Q5 of 8 Page 178

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

Given,

Diameter of circular plate = D = 56 cm


Radius of circular plate = R = 28 cm


Let, mass of the circular plate = M


Since density of plate is constant so,



We know,


Let centre of mass of the circular plate before removing the plate be at origin.


XCM= 0


Now,


Diameter of circular portion removed = d = 42 cm


Radius of circular portion = r = 21 cm


Let, mass of the circular portion removed = m1


Mass of the remaining portion = m2



From origin C.M. of circular portion removed lies at



Let, centre of mass of the remaining portion lie at a cm





Since density of plate is constant so,







Centre of mass of the remaining portion lie at 9 cm from initial centre of mass.


Negative sign shows that it lies left of the origin


More from this chapter

All 8 →
3

The moment of inertia of a triangular lamina of mass M and height h about its base is

 4

A man of mass m stands at one end of a plank of length l which lies at rest on a frictionless horizontal surface. The man walks to the other end of the plank. If the mass of the plank is m/3 the distance that the man moves relative to the ground will be _________

(a)


(b)


(c)


(d)

6

The speed of a motor increases from 1200rpm to 1800rpm in 20s. How many revolutions does it make in this period of time?

 7

A thin sheet of metal of uniform thickness is cut into the shape bounded by the line

x = a,


y = kx2


y = –kx2


Find coordinates of centre of mass.