A frictionless cart $A$ of mass $100\ kg$ carries other two frictionless carts $B$ and $C$ having masses $8\ kg$ and $4\ kg$ respectively connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart so that smaller cart do not move relative to it .......... $N$
$150$
$340$
$560$
$630$
In the figure shown $'P'$ is a plate on which a wedge $B$ is placed and on $B$ a block $A$ of mass $m$ is placed. The plate is suddenly removed and system of $B$ and $A$ is allowed to fall under gravity. Neglecting any force due to air on $A$ and $B$, the normal force on $A$ due to $B$ is
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
A block $B$ is placed on block $A$. The mass of block $B$ is less than the mass of block $A$. Friction exists between the blocks, whereas the ground on which the block $A$ is placed is taken to be smooth. $A$ horizontal force $F$, increasing linearly with time begins to act on $B$. The acceleration ${a_A}$ and ${a_B}$ of blocks $A$ and $B$ respectively are plotted against $t$. The correctly plotted graph is
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 $g = 10\, ms^{-2}$)
The value of $\frac{T_3}{T_1}$ is .............