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

The horizontal acceleration that should be given to a smooth inclined plane of angle $\sin^{-1} (1/l)$ to keep an object stationary on the plane relative to the inclined plane is

$A$ frictionless wire $AB$ is fixed on a circle of radius $R$. $A$ very small bead slips on this wire. The time taken by the bead to slip from $A$ to $B$ is:

Three blocks of masses $2m$,$4m$,and $6m$ are placed as shown in the figure. If $\sin 37^{\circ}=\frac{3}{5}$ and $\sin 53^{\circ}=\frac{4}{5}$,the acceleration of the system is:

Two masses $M_1$ and $M_2$ are arranged as shown in the figure. Let '$a$' be the magnitude of the acceleration of the system. If the mass of $M_1$ is doubled and that of $M_2$ is halved,then the new acceleration of the system is (Treat all surfaces as smooth; masses of pulley and rope are negligible).

$A$ block of mass $m$ is placed on a smooth fixed inclined plane with an angle of inclination of $37^{\circ}$. $A$ horizontal force $F$ is applied to keep the block at rest. Find the value of $F$.