question_answer

Two blocks, one of mass A = 1 kg and another B = 2 kg are shown in figure. A force of 5 N is applied on A. Coefficient of friction between A and B is 0.2 and that between B and horizontal surface is zero. Find the time taken for the front face of A to coincide with that of B.

A)  \[2\sqrt{2}s\]                   

B)  \[\sqrt{\frac{8}{3}}s\]

C)  \[\sqrt{\frac{3}{8}}s\]                  

D)  \[2s\]

Correct Answer: B

Solution :

                 The free body diagram of two blocks is shown in figure \[F-f=ma\] o             \[F-\mu N=ma\] Or           \[5-0.2\times 1\times 10=1\times {{a}_{A}}\] Or           \[{{a}_{A}}=3m/{{s}^{2}}\] This is the acceleration of A wrt B. The time taken for the front surface of A to coincide with that of B is \[s=ut+\frac{1}{2}{{a}_{A}}{{t}^{2}}\]     \[4=0+\frac{1}{2}\times 3\times {{t}^{2}}\] Or           \[{{t}^{2}}=\frac{8}{3}\] Or           \[t=\sqrt{\frac{8}{3}}s\]