System of Particles and Rotational Motion · Question 7

A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass M/8 is converted into a sphere of radius r and the larger part is converted into a circular disc of thickness t and radius 2R. If I1 is moment of inertia of a sphere having radius r about an axis through its centre and I2 is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia I2/I1= .

1. 35
2. 70
3. 140
4. 210

The position of an object having mass 0.1 kg as a function of time t is given as r= (10t2 i+5t3 j ) m. At t=1 s, which of the following statements are correct? Choose the correct answer from the options given below:

1. A, B and C only
2. B, C and D only
3. A, C and D only
4. A, B and D only

A particle is rotating in a circular path and at any instant its motion can be described as = 5t440- t33. The angular acceleration of the particle after 10 seconds is rad/s2.

1. 150
2. 120
3. 130
4. 170

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is m. (Take g=10 m/s2) [figure]

1. 3.33
2. 3.12
3. 2.22
4. 1.42

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