An object requires $500 \,N$ force to be pulled up on a $30^{\circ}$ frictionless smooth inclined plane at a constant speed. The weight of the object is

Two masses of $8\,kg$ and $4\,kg$ are connected by a string as shown in the figure over a frictionless pulley. The acceleration of the system is ............ $m/s^2$.

$A$ block of mass $200\, g$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F = \sqrt{x}\, N$ as shown in the figure. The value of $x = .....$

It is easier to draw up a wooden block along an inclined plane than to haul it vertically,principally because

Find the reading of the spring balance as shown in the figure. Assume that mass $M$ is in equilibrium and the block of mass $2.5 \text{ kg}$ is also in equilibrium. All surfaces are smooth. (Take $g = 10 \text{ m/s}^2$) (in $\text{ N}$)

Two smooth inclined planes $A$ and $B$ each of height $20 \ m$ have angles of inclination $30^{\circ}$ and $60^{\circ}$ respectively. If $t_1$ and $t_2$ are respectively the times taken by two blocks to reach the bottom of the planes $A$ and $B$ from the top,then $t_1 - t_2 = $ (Acceleration due to gravity $= 10 \ m \ s^{-2}$)