System of Particles and Rotational Motion

A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t=0 the cylinder has a translational velocity v0=49 m/s, perpendicular to its axis and a rotational velocity v0/4R about the centre. The time taken by the cylinder to start rolling is seconds. (coefficient of kinetic friction K=0.25 and g=9.8 m/s2)

1. 15
2. 5
3. 10
4. 7.5

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are and respectively.

1. 0.128 Nm, 100
2. 0.0128 Nm, 50
3. 0.128 Nm, 50
4. 0.0128 Nm, 100

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point (p) of normal bisector, as shown in the figure is . [figure]

1. ( 34, 1.25 )
2. ( 34, 1.0 )
3. (0, 0)
4. (1.25, 0)

A solid sphere (A) of mass 5m and a spherical shell (B) of mass m, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of aA and aB, respectively. The ratio of aA and aB is .

1. 5 : 21
2. 6 : 10
3. 21 : 25
4. 1 : 5

Two identical bodies A and B of equal masses have initial velocities v1=4 i m/s and v2=4 j m/s respectively. The body A has acceleration a1=6 i+6 j m/s2 while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in path.

1. circular
2. parabolic
3. straight line
4. elliptical

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle 1 and in the next 2 s it rotates through an angle 2. The ratio 2 1 is .

1. 6
2. 3
3. 4
4. 13

An object of uniform density rolls up the curved path with the initial velocity v0 as shown in the figure. If the maximum height attained by an object is 7v0210g (g = acceleration due to gravity), the object is a . [figure]

1. solid cylinder
2. ring
3. disc
4. solid sphere

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