Three rods each of mass m and length L are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

(1) $2{ \mathrm{mL}}^2$

(2) $\frac{m{L}^2}{2}$

(3) $\frac{m{L}^2}{3}$

(4) $\frac{m{L}^2}{6}$

A thin wire of length l and mass m is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be

(1) ml²

(2) Zero

(3) $\frac{m{l}^2}{{\pi }^2}$

(4) $\frac{m{l}^2}{2{\pi }^2}$

A meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor assuming that the end at the floor does not slip is (g=9.8 m/s²)

(1) 3.2 m/s

(2) 5.4 m/s

(3) 7.6 m/s

(4) 9.2 m/s

A circular disc of mass 2 kg and radius 10 cm rolls without slipping with a speed 2 m/s. The total kinetic energy of disc is

(1) 10 J

(2) 6 J

(3) 2 J

(4) 4 J

A horizontal disc rotating freely about a vertical axis through its centre makes 90 revolutions per minute. A small piece of wax of mass m falls vertically on the disc and sticks to it at a distance r from the axis. If the number of revolutions per minute reduce to 60 , then the moment of inertia of the disc is

(1) mr²

(2) $\frac{3}{2}m{r}^2$

(3) 2 mr²

(4) 3 mr²

The angular momentum of a particle performing uniform circular motion is L. If the kinetic energy of partical is doubled and frequency is halved, then angular momentum becomes

(1) $\frac{L}{2}$

(2) 2L

(3) $\frac{L}{4}$

(4) 4L

A uniform rod of mass m and length l is suspended by two strings at its ends as shown. When one of the strings is cut, the rod starts falling with an initial angular acceleration

(1) $\frac{g}{l}$

(2) $\frac{g}{2l}$

(3) $\frac{3g}{2l}$

(4) $\frac{3g}{4l}$

Two like parallel forces 20 N and 30 N act at the ends A and B of a rod 1.5 m long. The resultant of the forces will act at the point

(1) 90 cm from A

(2) 75 cm from B

(3) 20 cm from B

(4) 85 cm from A

A disc of mass m and radius r is free to rotate about its centre as shown in the figure. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height h, is

(1) $\sqrt{2gh}$

(2) $\sqrt{\frac{2}{3}gh}$

(3) $2\sqrt{\frac{gh}{3}}$

(4) $\frac{1}{2}\sqrt{3gh}$

When a body is rolling without slipping on a rough horizontal surface, the work done by friction is

(1) Always zero

(2) May be zero

(3) Always positive

(4) Always negative