In a physical balance working on the principle of moments,when $5\, mg$ weight is placed on the left pan,the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

$A$ wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However,the particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?

$A$ uniform rod $AB$ of length $\ell$ and mass $M$ is suspended from a point at a variable distance $x$ from end $A$,as shown. To keep the rod horizontal,a mass $m$ is suspended from its end $A$. $A$ set of $(m, x)$ values is recorded. The appropriate variables that give a straight line when plotted are:

An $L$-shaped object,made of two thin rods of uniform mass density and equal length $a$,is suspended from a string as shown in the figure. If $AB = BC = a$,and the angle made by $AB$ with the downward vertical is $\theta$,then:

$A$ hollow tilted cylindrical vessel of negligible mass rests on a horizontal plane as shown. The diameter of the base is $a$ and the side of the cylinder makes an angle $\theta$ with the horizontal. Water is then slowly poured into the cylinder. The cylinder topples over when the water reaches a certain height $h$,given by

$A$ horizontal beam is pivoted at $O$ as shown in the figure. Find the mass $m$ to make the scale straight in $kg$.