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

A man of the mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $\frac{\mathrm{M}}{3}$, the distance that the man moves relative to the ground is

1. $\frac{3\mathrm{L}}{4}$

2. $\frac{\mathrm{L}}{4}$

3. $\frac{4\mathrm{L}}{5}$

4. $\frac{\mathrm{L}}{3}$

Ratio of total kinetic energy and rotational kinetic energy in the motion of a disc is

1. 1:1

2. 2:7

3. 1:2

4. 3:1