Question

A block of mass $4kg$ is kept over a rough horizontal surface. The coefficient of friction between the block and the surface is $0.1$. At $t=0,\left(3\hat{i}\right)\frac{m}{s}$ velocity is imparted to the block and simultaneously $(-2\hat{i})N$ force starts acting on it. Its displacment in first $5s$ is

• A. $8\hat{i}$
• B. $-8\hat{i}$
• C. $3\hat{i}$
• D. $-3\hat{i}$

Answer 1

The correct option is C $3\hat{i}$

$f=\mu mg=0.1\times 4\times 10=4NNetforceinoppositedirectionofforce=F+f=2+4=6a_{deccelleartion}=\frac{6}{4}=\frac{3}{2}㎨v=0u-at=03-\frac{3}{2}t=0t=2secAftert=2secitwillstops=ut-\frac{1}{2}a{t}^{2}3\times 2-\frac{1}{2}\times \frac{3}{2}\times 4=3Aftert=1sec,FwillactuponitinoppositedirectionButF=2N<{\left(f_s\right)}_{max}=4NBlockwillremaininsameplace{s}_{displacement}=3\hat{i}$