A block of $7\,kg$ is placed on a rough horizontal surface and is pulled through a variable force $F$ (in $N$ ) $= 5\,t$ , where $'t'$ is time in second, at an angle of $37^o$ with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at $t = 0\,s$ . Find the time at which the block starts to slide ......... $\sec$ (Take $g = 10\,m/s^2$ )
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The block begins to slide if
$\mathrm{F} \cos 37^{\circ}=\mu\left(\mathrm{mg}-\mathrm{F} \sin 37^{\circ}\right)$
$5 t\left[\cos 37^{\circ}+\mu \sin 37^{\circ}\right]=\mu \mathrm{mg}$
$5 t\left[\frac{4}{5}+\frac{3}{5}\right]=70$ or $t=10$ second
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