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JEE 2020 Physics: System of Particles & Rotational Dynamics Quiz - 1 (06.08.2019)

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Question 1

A ring of mass m and radius R has three particles attached to it as shown in the figure. The center of the ring has speed v. The kinetic energy of the system is (Slipping is absent),

Question 2

The linear speed of a uniform spherical shell after rolling down an inclined plane of vertical height h from rest, is:

Question 3

A uniform solid sphere of radius R is placed on a rough horizontal surface and given a linear velocity v₀, angular velocity ω₀ as shown in the figure. The sphere comes to rest after moving some distance to the right. It follows that:

Question 4

A body kept on a smooth horizontal surface is pulled by a constant horizontal force applied at the top point of the body. If the body rolls purely on the surface, its shape can be:

Question 5

A uniform cylinder of radius R is spinned about its axis to the angular velocity

and then placed into a corner, see figure. The coefficient of friction between the corner walls and the cylinder is

. How many turns will the cylinder accomplish before it stops?

Question 6

A billiard ball of Radius R, initially at rest is given a sharp impulse b a cue. The cue is held horizontally at a distance h above the central line as shown in the figure. The ball leaves the cue with speed

. It rolls and slides while moving forward and eventually acquires a final speed of

. What is the relation between h and R?

Question 7

A wheel of moment of inertia 2 Kg m² is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 radii& Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is

Question 8

A tire of radius R rolls on a flat surface with angular velocity ω and velocity ν as shown in the diagram. If ν > ωR, in which direction does friction from the tire act on the road?

Question 9

A particle moving on a horizontal frictionless plane collides elastically with a uniform smooth rod lying on the same plane and which is hinged to rotate about a vertical axis passing through one of its ends. Then,

Question 10

A system of N particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?

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