A block is placed on a smooth inclined plane as shown. For what value of horizontal force $F,$ the block will remain at rest?

Figure shows a small ball of mass $m$ held at rest by means of two light and inextensible strings. The tensions in the inclined string at the instant shown and just after cutting the horizontal string are respectively

In the arrangement shown, what is the normal reaction between the block $A$ (mass $=5 \mathrm{kg}$ ) and ground?

Find the ratio of the extension in upper spring to lower spring.

The system shown below is in equilibrium. Find the acceleration of block $m_1,$ immediately after spring $k_2$ is cut.

At a certain moment of time, acceleration of the block $A$ is $2 \mathrm{m} {\mathrm{s}}^{-2}$ upward and acceleration of block $B$ is $3 \mathrm{m} {\mathrm{s}}^{-2}$ upward. The acceleration of block $C$ is (masses of pulleys and string are negligible)

Figure shows an arrangement of blocks, pulley and strings. Strings and pulley are massless and frictionless. The relation between acceleration of the blocks as shown in the figure is

In the figure shown, two blocks of masses $2 \mathrm{kg}$ and $4 \mathrm{kg}$ are connected by a massless string which is just taut ($i.e.,$ tension is zero at this moment). Now two forces $4 \mathrm{N}$ and $15 \mathrm{N}$ are applied on blocks. The tension in the string is (coefficient of static and kinetic friction are same). $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

A block of mass $m$ is kept on a plank. The coefficient of friction between the plank and block is $1.$The plank is slowly raised from one end so that it makes angle $\theta$ with horizontal. The forces of friction acting on the plank, when $\theta =30°$ and $\theta =60°$are respectively,