$A$ 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 $x = .....$

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:

$A$ block of mass $m_1 = 2\,kg$ on a smooth inclined plane at an angle of $30^\circ$ is connected to a second block of mass $m_2 = 3\,kg$ by a cord passing over a frictionless pulley as shown in the figure. The acceleration of each block is ....... $m/s^2$ (assume $g = 10\,m/s^2$).

$A$ frictionless wire $AB$ is fixed on a sphere of radius $R$. $A$ very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is

$A$ solid sphere,a hollow sphere,and a ring are released from the top of a frictionless inclined plane,causing them to slide down the plane. For which object is the acceleration down the plane the maximum?

$A$ small block slides without friction down an inclined plane starting from rest. Let $S_n$ be the distance travelled from time $t = n - 1$ to $t = n$. Then $\frac{S_n}{S_{n+1}}$ is