$A$ uniform rod of mass $15\,kg$ and length $5\,m$ is held stationary with the help of a light string as shown. The tension in the string is ......... $N.$

$A$ uniform meter scale is balanced at the $30 \ cm$ mark on a knife edge,when weights of $60 \ N$ and $10 \ N$ are suspended at the $10 \ cm$ and $80 \ cm$ marks,respectively. The mass of the meter scale is: $(g = 10 \ m/s^2)$ (in $kg$)

$A$ 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

$A$ uniform rod of mass $250 \ g$ having length $100 \ cm$ is balanced on a sharp edge at $40 \ cm$ mark. $A$ mass of $400 \ g$ is suspended at $10 \ cm$ mark. To maintain the balance of the rod,the mass to be suspended at $90 \ cm$ mark is: (in $g$)

$A$ 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?

Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body,which is then pivoted as shown in the figure. If in equilibrium the body is in the shown configuration,the ratio $M/m$ will be