A mass $m$ hangs with the help of a string wrapped around a pulley on a firctionless  bearing. The pulley has mass $m$ and radius $R$. Assuming pulley to be a perfect  uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the  pulley, is:-

Figure below shows a shampoo bottle in a perfect cylindrical shape. In a simple experiment, the stability of the bottle filled with different amount of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle $\theta$ depicts the critical angular displacement resulting, in the bottle losing its stability and tipping over. Choose the graph correctly depicting the fraction $f$ of shampoo filled $(f=1$ corresponds to completely filled) versus the tipping angle $\theta$

A heavy iron bar, of weight $\mathrm{W}$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is:

$A$ thin rod of length $L$ is placed vertically on a frictionless horizontal floor and released with a negligible push to allow it to fall. At any moment, the rod makes an angle $\theta$ with the vertical. If the center of mass has acceleration $= A$, and the rod an angular acceleration $= \alpha$ at initial moment, then

$A$ rod of weight $w$ is supported by two parallel knife edges $A$ and $B$ and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at a distance $x$ from $A$.

Two particles of mass $m$ each are fixed at the opposite ends of a massless rod of length $5m$ which is oriented vertically on a smooth horizontal surface and released. Find the displacement of the lower mass on the ground when the rod makes an angle of $37^o$ with the vertical. ........ $m$