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 $........\,s$

Two blocks of mass $M$ and $m$ are kept on the trolley whose all surfaces are smooth select the correct statement

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 ....... $N$ $(g = 10\,\,m/s^2)$

A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of  inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is

Consider the following statements about the blocks shown in the diagram that are being pushed by a constant force on a frictionless table

$A.$All blocks move with the same acceleration

$B.$The net force on each block is the same

Which of these statements are/is correct

A wooden wedge of mass $M$ and inclination angle $(\alpha)$ rest on a smooth floor. A block of mass $m$ is kept on wedge. A force $F$ is applied on the wedge as shown in the figure such that block remains stationary with respect to wedge. So, magnitude of force $F$ is