Persons $A$ and $B$ are standing on the opposite sides of a $3.5 \,m$ wide water stream which they wish to cross. Each one of them has a rigid wooden plank whose mass can be neglected. However,each plank is only slightly longer than $3 \,m$. So,they decide to arrange them together as shown in the figure. With $B$ (mass $17 \,kg$) standing on one end of the plank,the maximum mass of $A$,who can walk over the plank is close to ............ $kg$.

$A$ uniform rod of length $L$ and weight $W$ is suspended horizontally by two vertical ropes as shown. The first rope is attached to the left end of the rod while the second rope is attached at a distance $L/4$ from the right end. The tension in the second rope is

$A$ car weighs $1800 \, kg$. The distance between its front and back axles is $1.8 \, m$. Its centre of gravity is $1.05 \, m$ behind the front axle. The force exerted by the level ground on each back wheel is ....... $N$.

$A$ 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?

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

Find the value of $T_1$ (in $N$),if the system is in equilibrium and the mass of the rod is $10 \ kg$ and its length is $10 \ m$. $[g = 10 \ m/s^2]$ (in $N$)