question_answer

                A block of mass 10 kg is placed on a rough horizontal surface having coefficient of friction \[\mu \] = 0.5. If a horizontal force of 100 N is applied on it, then the acceleration of the block wilt be: \[(g=10\,m/{{s}^{2}})\]

A)                                                                                                                                                                                            \[15\,\,m/{{s}^{2}}\]

B)                 \[10\,\,m/{{s}^{2}}\]

C)                 \[5\,\,m/{{s}^{2}}\]  

D)                 \[0.5\,\,m/{{s}^{2}}\]

Correct Answer: C

Solution :

                Key Idea: Apply Newton's second law along x-axis.                                 Free body diagram of block is:                 From Newton's second law along x-axis                 \[\Sigma {{F}_{x}}=ma\] \[i.e.,F-f=ma\] \[orF-\mu mg=ma\] \[ora=\frac{F-\mu mg}{m}\]                 Given, F = 100 N, \[\mu \] = 0.5, m = 10 kg, \[g=10\,m/{{s}^{2}}\]                 Substituting die values in the above relation for acceleration of block,                 \[a=\frac{(100)-(0.5)\,(10)\,(10)}{(10)}=5\,m/{{s}^{2}}\]