A Wheel has an angular acceleration of 3.0 rad/s² and an initial angular speed of 2.00 rad/s. In a time of 2s it has rotated thorough an angle (in radian) of:

• 6

• 10

• 12

• 12

A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A  is ml²/3, the initial angular acceleration of the rod will be:

• 2g/3l

• mgl/2

• 3gl/2

• 3gl/2

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is L_A when it is at A and L_B when it is B, then: 

• L_A > L_B

• L_A = L_B

• the relationship between L_A and L_B depends upon the slope of the line AB

• the relationship between L_A and L_B depends upon the slope of the line AB

One end of a string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards centre) will be (T represents the tension in the string)

• T

• 
• 
• 

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of the disc with angular velocities ω₁ and ω₂. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

• Angular velocity

• Moment of inertia

• Angular momentum

• Rotational Kinetic energy

Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

• W_C > W_B> W_A

• W_A > W_B > W_C

• W_A>W_C>W_B

• W_B>W_A>W_C

128.

A uniform rod of length l is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest from its unstable equilibrium position. When, it has turned through an angle θ, its angular velocity ω is given by

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{I}}\right)} \sin \frac{\mathrm{\theta }}{2}$

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{I}}\right)} \cos \frac{\mathrm{\theta }}{2}$

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{I}}\right)} \sin \mathrm{\theta }$

• $\sqrt{\left(\frac{6\mathrm{g}}{\mathrm{l}}\right)} \cos \mathrm{\theta }$

ABC is the right-angled triangular plane of uniform thickness. The sides are such that AB>BC as shown in the figure. I₁, I₂, I₃ are moments of inertia about AB, BC and AC, respectively. Then which of the following relations is correct?

• I₁ = I₂ = I₃

• I₂ > I₁> I₃

• I₃<I₂<1₁

• I₃>I₁>I₂

An ice-berg of density 900 kgm^-3 is floating in the water of density 1000 kgm^-3. The percentage of the volume of ice-berg outside the water is

• 20%

• 35%

• 10%

• 11%