A block of mass $M$ is at rest on a plane surface inclined at an angle $\theta$ to the horizontal. The magnitude of force exerted by the plane on the block is

Figure shows a uniform rod of length $30 \,cm$ having a mass $3.0 \,kg$. The rod is pulled by constant forces of $20 \,N$ and $32 \,N$ as shown. Find the force exerted by $20 \,cm$ part of the rod on the $10 \,cm$ part (all surfaces are smooth) is ......... $N$

Two blocks of  $7\,\,kg$ and $5\,\,kg$  are connected by a heavy rope of mass $4\,\,kg.$ An upward force of $200\,N$  is applied as shown in the diagram. The tension at the top of heavy rope at point $P$  is ....... $N$ $(g = 10\,\,m/s^2)$

Consider the shown arrangement. Assume all surfaces to be smooth. If $N$ represents magnitudes of normal reaction between block and wedge, then acceleration of $M$ along horizontal equals

$Assertion$ : A man and a block rest on smooth horizontal surface. The man holds a rope which is connected to block. The man cannot move on the horizontal surface

$Reason$ : A man standing at rest on smooth horizontal surface cannot start walking due to absence of friction (The man is only in contact with floor as shown).

A block '$A$' takes $2\,s$ to slide down a frictionless incline of $30^{\circ}$ and length ' $l$ ', kept inside a lift going up with uniform velocity ' $v$ '. If the incline is changed to $45^{\circ}$, the time taken by the block, to slide down the incline, will be approximately $........\,s$