Let g be acceleration due to gravity on the surface of earth and T be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2%. Keeping all other quantities same (even $\omega$)

1.  g decreases by 2% and T decreases by 4%

2.  g decreases by 4% and T decreases by 2%

3.  g increases by 4% and T decreases by 4%

4.  g decreases by 4% and T increases by 4%

The angular momentum of a system of particles is conserved

1. when no external force acts upon the system

2. when no external torque acts upon the system

3. when no external impulse acts upon the system

4. when axis of rotation remains same

One hollow and one solid cylinder of the same radius roll down on a smooth inclined plane. Then the foot of the inclined plane is reached by 

1.  solid cylinder earlier 

2.  hollow cylinder earlier 

3.  simultaneously both 

4.  the heavier earlier irrespective of being solid or hollow

A loaded truck has to take a sharp turn to the left. The center of gravity of the truck can be altered by shifting the concentrated load. To avoid toppling, the load must be shifted 

1.  up and left 

2.  up and right 

3.  down and left 

4.  down and right

ABC is an equilateral triangle with O as its cente. ${\overrightarrow{F}}_1, \overrightarrow{F_2} and \overrightarrow{F_3}$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\overrightarrow{F_3}$ is

1. $F_1+F_2$

2. $F_1-F_2$

3. $\frac{F_1+F_2}{2}$

4. $2(F_1+F_2)$

A circular platform is mounted a frictionless vertical axle. Its radius R = 2m and moment of inertia about the axle are 200 ${\mathrm{kgm}}^2$. It is initially at rest. A 50 kg man on the edge of the platform and begins to walk along the edge at the speed of 1 $m{s}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is

1.  $\mathrm{\pi s}$

2.  $\frac{3\mathrm{\pi }}{2}s$

3.  $2\mathrm{\pi s}$

4.  $\frac{\mathrm{\pi }}{2}\mathrm{s}$

$If F be a force acting on a particle having the position vector r and \tau be the torque of the force about the origin, then;$
$\left(a\right) r.\tau =0 and F.\tau =0 \left(b\right) r.\tau =0 and F.\tau \ne 0$
$\left(c\right) r.\tau \ne 0 and F.\tau \ne 0 \left(d\right)r.\tau \ne 0 and F.\tau =0$ 

A T joint is formed by two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment of inertia about axis passing through A and perpendicular to the plane of the joint,

1.  $\frac{2{\mathrm{mL}}^2}{3}$

2.  $\frac{{\mathrm{mL}}^2}{12}$

3.  $\frac{{\mathrm{mL}}^2}{6}$

4.  None of these

The moment of inertia of a loop of radius R and mass M, about any tangent line in its plane will be

1. $\frac{3M{R}^2}{2}$

2. $\frac{M{R}^2}{2}$

3. $M{R}^2$

4. $\frac{M{R}^2}{4}$

A hollow sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity v = 0.5 m/ s. The kinetic energy of the sphere is

1.  0.1 J

2.  0.3 J

3.  0.5 J

4.  0.42 J