A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ}$ with an acceleration of $\frac{g}{2}$, the value of coefficient of kinetic friction is

A body of mass $m$ is suspended by two strings making angles $\theta_1$ and $\theta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3} T_2$, the angles $\theta_1$ and $\theta_2$ are

A block of mass 1 kg , moving along $x$ with speed $v_i=10 \mathrm{~m} / \mathrm{s}$ enters a rough region ranging from $x=0.1 \mathrm{~m}$ to $x=1.9 \mathrm{~m}$. The retarding force acting on the block in this range is $\mathrm{F}_{\mathrm{r}}=-\mathrm{kr} \mathrm{N}$, with k $=10 \mathrm{~N} / \mathrm{m}$. Then the final speed of the block as it crosses rough region is.

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively, are (in N ) :

(Take acceleration due to gravity $10 \mathrm{~m} / \mathrm{s}^2$ )