Chapter 7: System of Particles and Rotational Motion

For which of the following does the centre of mass lie outside the body?

Which of the following points is the likely position of the centre of mass of the system shown in the figure

A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +ve y-axis and intersecting z-axis at z = a. The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is

a)

b)

c)

d)

When a disc rotates with uniform angular velocity, which of the following is not true?

A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind. The moment of inertia about the z-axis is then

a) increased

b) decreased

c) the same

d) changed in an unpredicted manner

In problem 7.5. the CM of the plate is now in the following quadrant of the x-y plane

a) I

b) II

c) III

d) IV

The density of a non-uniform rod of length 1 m is given by
where a and b are constant and 0 ≤ x ≤ 1. The centre of mass of the rod will be at

a)

b)

c)

d)

A merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the ground, radially away from the centre of the round. The speed of the round afterwards is

a) 2ω

b) ω

c) ω/2

d) 0

Choose the correct alternatives:

Figure shows two identical particles 1 and 2, each of mass m, moving in opposite directions with the same speed v along parallel lines. At a particular instant, r1 and r2 are their respective positions vectors drawn from point A which is in the plane of the parallel lines. Choose the correct options: