For the given figure,find the acceleration of the $1\, kg$ block. The string is massless,the mass of the pulley is $M = 2\, kg$,and the diameter of the pulley is $0.2\, m$. (in $m/s^2$)

$A$ truck is moving at a speed of $54 \ km/h$. The radius of its wheels is $50 \ cm$. If the wheels come to rest after $20$ rotations upon applying brakes,what is the linear distance covered by the truck during this time? What is the angular acceleration of the wheels?

$A$ ring of mass $m$ can freely slide along the massless curved rod as shown. At the lower most point,the curved path becomes vertical. If the whole system is released from rest,what is the velocity of the ring $(v)$ at the lowermost point just before touching the block $M$ (all surfaces are smooth)?

$A$ solid cylinder of mass $M$ and radius $R$ is placed in a horizontal position. Two strings are wrapped around the cylinder. Find the tension in the strings and the acceleration of the cylinder as the strings unwind.

$A$ uniform rod is rotating in a gravity-free region with a certain constant angular velocity $\omega$. The variation of tensile stress $\sigma$ with distance $x$ from the axis of rotation is best represented by which of the following graphs?

$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid on the tube at the other end is