A sphere is rolling down a plane of inclination $\theta$ to the horizontal.  The acceleration of its centre down the plane is 

1. g sin $\theta$                   

2. less than g sin $\theta$

3. greater than g sin $\theta$

4. zero

  

A bob of mass m attached to an inextensible string of length l is suspended from vertical support.  The bob rotates in a horizontal circle with an angular speed $\mathrm{\omega }$ $\mathrm{rad}/\mathrm{s}$ about the vertical.  About the point of suspension.

In free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M at a distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet - block system is at a distance of

1. $\frac{(D-d)}{M+m}$ from the bullet

2. $\frac{md+MD}{M+m}$ from the block

3. $\frac{2md+MD}{M+m}$ from the block

4. $\frac{(D-d)M}{M+m}$ from the bullet

Blocks A and B are resting on a smooth horizontal surface given equal speeds of 2 m/s in the opposite sense as shown in the figure.

At t = 0, the position of blocks are shown, then the coordinates of centre of mass at t = 3s will be 

1.  (1, 0)

2.  (3, 0)

3.  (5, 0)

4.  (2.25, 0)

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

1. 800 rad

2. 400 rad

3. 200 rad

4. 100 rad

A force\(- F \hat k\) acts on O, the origin of the coordinate system. The torque at the point (1, -1) will be:

1. $-\mathrm{F}\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$

2. $\mathrm{F}\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$

3. $-\mathrm{F}\left(\hat{\mathrm{i}}-\hat{\mathrm{j}}\right)$

4. $\mathrm{F}\left(\hat{\mathrm{i}}-\hat{\mathrm{j}}\right)$

Moment of inertia of an object does not depend upon

1.  mass of object

2.  mass distribution

3.  angular velocity

4.  axis of rotation

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity $\omega$. Another disc of the same dimensions but of mass $\frac{1}{4}M$ is placed gently on the first disc co-axially. The angular velocity of the system will be:

1.  $\frac{2}{3}\mathrm{\omega }$

2.  $\frac{4}{5}\mathrm{\omega }$

3.  $\frac{3}{4}\mathrm{\omega }$

4.  $\frac{1}{3}\mathrm{\omega }$

When a torque acting upon a system is zero, then which of the following will be constant 

1.  force

2.  Linear momentum

3.  Angular momentum

4.  Linear impulse

Consider a system of two particles having masses ${\mathrm{m}}_1 \mathrm{and} {\mathrm{m}}_2$. If the particle of mass ${\mathrm{m}}_1$ is pushed towards the center of mass of particles through a distance, by what distance would be the particle of the mass ${\mathrm{m}}_2$ move so as to keep the center of mass of particles at the original position?

1.  $\frac{{\mathrm{m}}_1}{{\mathrm{m}}_1 + {\mathrm{m}}_2}\mathrm{d}$

2.  $\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}\mathrm{d}$

3.  d

4.  $\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}\mathrm{d}$