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 wedge of height $H$ (fixed) and inclination $\alpha $ (variable) is moving on a smooth horizontal surface with constant acceleration $g\ m/s^2$ . A small block is placed at bottom of incline as shown in figure, slips on the smooth surface of incline . Choose $CORRECT$ statement about time taken by block to reach the top of incline

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in figure. The whole system is going upwards with an acceleration of $2\, ms^{-2}$. The tensions $T_1$ and $T_2$ are respectively (Take $g = 10\, ms^{-2}$)

$Assertion$ : 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).

Three identical blocks of masses $m=2\; k g$ are drawn by a force $F=10.2\; N$ with an acceleration of $0.6\; ms ^{-2}$ on a frictionless surface, then what is the tension (in $N$) in the string between the blocks $B$ and $C$?

Three solids of masses ${m_1},\,{m_2}$ and ${m_3}$ are connected with weightless string in succession and are placed on a frictionless table. If the mass ${m_3}$ is dragged with a force T, the tension in the string between ${m_2}$ and ${m_3}$ is