System of Particles and Rotational Motion · Question 11

Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius R about an axis parallel to AB axis with separation of 3 m as shown in figure below. The value of R is given as 2. The value of is . [figure]

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43 105 dyne.cm, the angular acceleration of the discs about the given axis AB is rad/s2. [figure]

1. 100
2. 22
3. 27
4. 11

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n cm. The value of n is

When the position vector r = x i + y j + z k changes sign as - r, which one of the following vector will not flip under sign change?

1. Velocity
2. Linear momentum
3. Acceleration
4. Angular momentum

A flywheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is J. (g = 10 m/s2)

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is kg m2. (g = 9.8 m/s2)

1. 8.3 10-3
2. 4.75 10-3
3. 1.86 10-2
4. 9.5 10-3

A thin uniform rod (X) of mass M and length L is pivoted at a height ( L3 ) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is . (g = gravitational acceleration) [figure]

1. 32 gL
2. 3gL
3. 3 2 gL
4. 1 2 gL

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I1. A small concentric cylinder of length L/2 and radius R/3 carved from this cylinder has moment of inertia about its axis equal to I2. The ratio I1/I2 is .

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :

1. 43 Lmd2
2. 32 Lmd2
3. 2L5md2
4. 2Lmd2

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (R < L) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M):

1. 34MR2 + 16ML2
2. 38MR2 + 712ML2
3. 34MR2 + 712ML2
4. 38MR2 + 16ML2