A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the co-efficient of static friction between the block on the floor with the floor itself is

A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force $\mathrm{F}=20 \mathrm{~N}$ acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take $\mathrm{g} \simeq 10 \mathrm{~ms}^{-2}$ )

A block of certain mass is placed on a rough inclined plane. The angle between the plane and the horizontal is 30$^\circ$. The coefficients of static and kinetic frictions between the block and the inclined plane are 0.6 and 0.5 respectively. Then, the magnitude of the acceleration of the block is [Take g = 10 ms$^{-2}$]

A body of mass $$10 \mathrm{~kg}$$ is kept on a horizontal surface. The coefficient of kinetic friction between the body and the surface is 0.5. A horizontal force of $$60 \mathrm{~N}$$ is applied on the body. The resulting acceleration of the body is about

Two masses of $$5 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ are suspended with the help of massless inextensible strings as shown in figure below.

When whole system is going upwards with acceleration $$2 \mathrm{~m} / \mathrm{s}^2$$, the value of $$T_1$$ is (use, $$g=9.8 \mathrm{~m} / \mathrm{s}^2$$)

An object with mass $$5 \mathrm{~kg}$$ is acted upon by a force, $$\mathbf{F}=(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \mathrm{N}$$. If its initial velocity at $$t=0$$ is $$\mathbf{v}=(3 \hat{\mathbf{i}}+12 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$$, the time at which it will just have a velocity along $$y$$-axis is -