System of Particles and Rotational Motion · Question 2

List-I shows four planar structures made of uniform solid rods each of mass m and length l. In the List-II the possible moment of inertia of these structures about an axis OCO', which lies in the plane of the structures, are given. Choose the option that describes the correct match between the entries in List-I to those in List-II.

1. P→5, Q→1, R→4, S→2
2. P→1, Q→3, R→4, S→2
3. P→5, Q→3, R→2, S→1
4. P→5, Q→4, R→2, S→1

After the collision the disk starts to rotate around point C in the XY plane. The maximum change in the height (in m) of its center O is:

Amount of energy loss (in J) in the collision is:

A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius R/2 is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed . If the angular speed at which the large disc rotates is /n, then the value of n is . [figure]

A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x=L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is . [figure]

If the collision occurs at time t0 = 0, the value of vcm/(a ) will be .