A uniform disc of mass $M$ and radius $R$ is released from rest in the shown position. $PQ$ is a string, $OP$ is a horizontal line, $O$ is the centre of the disc and distance $OP$ is $\frac{R}{2}.$ Then tension in the string just after the disc is released will be:

A uniform square plate of mass $m$ is supported, as shown. If the cable suddenly breaks, then the angular acceleration of the plate is

Figure shows a uniform disc, with mass $\mathrm{M}=2.4 \mathrm{kg}$ and radius $\mathrm{R}=20 \mathrm{cm}$, mounted on a fixed horizontal axle. A block of mass $\mathrm{m}=1.2 \mathrm{kg}$ hangs from a massless cord that is wrapped around the rim of the disc. The tension in the cord is

A uniform ladder of length $5 \mathrm{m}$ is placed against the wall in vertical plane as shown in the figure. If coefficient of friction $\mathrm{\mu }$ is the same for both the wall and the floor then minimum value of $\mathrm{\mu }$ for it not to slip is 

A uniform rod of length $4L$ and mass $M$ is suspended from a horizontal roof by two light strings of length $L$ and $2L$ as shown. Then the tension in the left string of length $L$ is

A rod of mass $m$ is supported by string $AB$ and friction due to the wall. Then friction force on rod due to the wall is: ($g=$acceleration due to gravity)